Consider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, what is true about the other zero

Answers

Answer 1

Answer:

Step-by-step explanation:

irrational roots always occur in pairs.

Other root is also irrational and is negative of first zero.

Answer 2

If a quadratic equation with integer coefficients and two distinct roots have one irrational root then another root is also irrational .

What is quadratic equation ?

Any equation of the  form [tex]ax^{2}+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called quadratic equation .

Let assume quadratic equation is

[tex]ax^{2}+bx+c=0[/tex]

Given that coefficients are integer and roots are distinct

we know root of quadratic equation are

[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

As roots are distinct

[tex]b^2-4ac > 0\\[/tex]

and one root is irrational so [tex]b^2-4ac[/tex] is not a perfect square

Hence another root is also irrational .

If a quadratic equation with integer coefficients and two distinct roots have one irrational root then another root is also irrational .

To learn more about quadratic equations visit : https://brainly.com/question/1214333


Related Questions

How does Ray Bradbury's description of Margot's appearance in "All Summer in a Day" also give insight into her feelings?

Answers

Answer:

The description of Margot as a frail girl who had lost her vibrancy shows that she was in eager anticipation of the rain.

Step-by-step explanation:

The short story, "All Summer in a Day", tells of how a girl named Margot always stood differently from her classmates because she eagerly anticipated a time when the sun will come out as the scientists projected. It had been raining in this planet, Venus for seven years non-stop.

Margot who came from planet earth some five years ago could still clearly recall how the sun looked like and despite her description of it, the children still doubted her. On the day the sun finally came, the children locked Margot in a closet and she was unable to see the sun.

Heeeelp me Asp need this

Answers

Answer:

False; True; True

Step-by-step explanation:

If the radius is 4, the area of the circle is

pi*r*r = pi * 4 * 4 = 16pi; The second statement is true.

The entire circle's "angle" is 2pi, so the sector takes (2pi/3) / 2pi of it all, equal to 1/3 of the entire circle - hence the area of the sector is

16pi * 1/3 = 16pi/3; the first statement is false

The length of the entire circle is 2 * pi * r = 2 * pi * 4 = 8pi

The sector is 1/3 of that, so 8pi/3; the third statement is true.

What method could be used to prove the triangle congruent?

Answers

Answer:SSS

Step-by-step explanation:

Answer:

asa ,.............................

Evaluate each expression
7 + 9=
43 - 5=

Answers

The answer you just add and subtract
7+9=16
43-5=38
7+9= 16
43-5= 38
Explained: it’s pretty easy lol

Which of the following rational numbers is the largest? A. 0.9 B. -8/9 C. -2 1/2 D. 9/4​

Answers

Answer:

i think its - 2/1/2 hope its correct

La suma de dos números enteros que tienen signos diferentes es:

Answers

1 Si los sumandos son del mismo signo, se suman los valores absolutos y al resultado se le pone el signo común. 2 Si los sumandos son de distinto signo, se restan los valores absolutos (al mayor le restamos el menor) y al resultado se le pone el signo del número de mayor valor absoluto.

Answer:

Hhhhhhhhnnnnnnnnnn

Step-by-step explanation:

Bbb


Jaden cut a square sheet of paper in half along a diagonal to make two equal
triangles. Each triangle has an area of 0.08 square units. What is the length,
in units, of one side of the square?

Answers

If each triangle is 0.08 then the area of the square would be 0.16 a square has 4 sides
0.16/4 = 0.04

The length of one side of the square is approximately 0.4 units.

Let's assume that the side length of the square is "s" units.

When the square sheet of paper is cut in half along the diagonal, it forms two equal right-angled triangles. The area of each triangle is given as 0.08 square units.

The formula for the area of a right-angled triangle is:

Area = (1/2) * base * height

Since the triangles are equal, we can write:

0.08 = (1/2) * base * height

Now, let's find the base and height of one of the triangles. Since the triangle is a right-angled triangle, the base and height are the legs of the triangle.

Let's assume the base and height of one triangle are "b" and "h," respectively.

0.08 = (1/2) * b * h

We are given that the area of each triangle is 0.08 square units, so we can write:

0.08 = (1/2) * s * s

Now, we can solve for "s":

[tex]s^2 = 0.08 * 2\\s^2 = 0.16[/tex]

Take the square root of both sides:

[tex]s = \sqrt{0.16}\\s \approx 0.4[/tex]

So, the length of one side of the square is approximately 0.4 units.

To know more about square:

https://brainly.com/question/32865510

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A cube has a volume of 64. What is the side length of one side
#15

Answers

Answer:

4

Step-by-step explanation:

volume is equal to a x a x a

This means that [tex]a^{3}[/tex] = V

Therefore, a = cube root of V, which is 4

It would be 4.

Using the formula
V=a3
Solving fora
a=V⅓=64⅓≈4

Please answer ASAP I need to know

Answers

Here is my answer. I hope this is helpful.

Enter the number that belongs in the green box

Answers

Answer:

60

Step-by-step explanation:

Jonah took out a four year loan for $22,000 to help pay for college. He has to pay 5% simple interest on the loan. How much will he have to pay back at the end of the four years?

Answers

Answer:

26,400

Step-by-step explanation:

1) Find 5% of 22,000 by multiplying 22,000 by .05. You should get 1100.

2) Multiply that by 4. (4400)

3) Now add that to the original.

Find the absolute value.

1 -31=___

-1 121=___

-1 -221=___

Answers

I guess we will never know

Answer:

-30

120

-222

Step-by-step explanation:

help please!!
[tex]\text{solve the following equation : }[/tex]
[tex] \sf\tan^{2}(\theta)-(1+\sqrt{3})\tan(\theta)+\sqrt{3} = 0[/tex]

Answers

tan²( θ ) - (1 + √3) tan (θ) + √3 = 0

tan²( θ ) - (tan (θ) + √3 tan (θ)) + √3 = 0

tan²( θ ) - tan (θ) - √3 tan (θ) + √3 = 0

tan( θ ) ( tan (θ) - 1) - √3 ( tan (θ) - 1 ) = 0

( tan( θ ) - 1 ) ( tan( θ ) - √3 ) = 0


tan( θ ) - 1 = 0

θ = π/₄

tan( θ ) - √3 = 0


θ = π/₃


so θ = π/₄ and θ = π/₃

Answer:

[tex] \huge \boxed{ \red{ \boxed{\begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} }}}[/tex]

Step-by-step explanation:

to understand thisyou need to know about:trigonometryPEMDASlet's solve:

distribute tan(θ):

=>tan²(θ)-(tan(θ)+√3tan(θ))+√3=0

remove parentheses:

=>tan²(θ)-tan(θ)-√3tan(θ)+√3=0

so this equation is now in standard form i.e ax²+bx+c=0

we can solve by factoring as we solve quadratic equation

factor out tanθ:

=>tan(θ)(tan(θ)-1)-√3tan(θ)+√3=0

factor out -√3:

=>tan(θ)(tan(θ)-1)-√3(tan(θ)-1)=0

group:

=>(tan(θ)-√3)(tan(θ)-1)=0

separate it as two different equation:

[tex] \implies \begin{cases} \tan( \theta) - 1 = 0 \\ \tan( \theta) - \sqrt{3} = 0 \end{cases}[/tex]

add 1 and √3 to both sides to first and second equation respectively:

[tex] \implies \begin{cases} \tan( \theta) - 1 + 1 = 0 + 1 \\ \tan( \theta) - \sqrt{3} + \sqrt{3} = 0 + \sqrt{3} \end{cases} [/tex]

[tex] \implies \begin{cases} \tan( \theta) = 1 \\ \tan( \theta) = \sqrt{3} \end{cases} [/tex]

[tex] \therefore \begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} [/tex]


Understanding Intercepts
What is the x-value of the y-intercept? How do you
know?

Answers

Answer:

0

Step-by-step explanation:

The x-value in the y-intercept must be zero. This is because the y-intercept is where a line or function intersects with the y-axis. All points on the y-axis have an x-value of 0. Therefore, all y-intercepts will have an x-value of 0 and look like (0,b).

Answer: x and y intercepts are the points in which your line crossing x axcis and y axcis . For the streight line given by  linear function y=ax+b we find coordinates of the point A represent x intercept  using value for the second coordinate y=0 then return this value to linear function

0=ax+b       subtract b from both sides

-b     -b

-b=ax          divide by a which id different then 0

-b/a=x

X-itercept is a point A(-b/a, 0)

 

For y intercept point B (x.y) our first coordinate x=0, return this value to the linear function y=ax+b

y=a*0+b  

Y=0+b

y=b

y intercept is a point B(0,b)

For the special types of linear equations:

1. When a=0 liner function is y=b we have parallel lines with x axcise, crosing only y axcise and there are only y intercept B(0,b)

2. When a=0 and b=0 linear function is y=0, which is equation of the x axcise. In this case y intercept is the orgin point O(0,0) and x-intercepts is are all points of the x axcise A(x,0); x can be any real number. This means infinite many x intercept points.

3. When a is not 0 and b=0 we have x intercept point A(0,0) and y intercept point B(0,0).

4. For the linear equation x=c, c is constant value, we have parallel line with y axcise crosing x axcise at the point A(c,0) and there is no y intersect because there are parallel lines

Step-by-step explanation:     Example y=2x+6. For x intercept  y=0, return to linear function and in the place oy poot its value  

               0=2x+6    subtract  6

              -6      -6

              -6=2x          divide by 2

              -3=x                                                                                                      

X intercept points is a point A(-3,0)                                                                                                                        

For the y intercept point B(x,y)  x=0, return to linear function and in the place of x poot its value

              y=2x+6

              y=2*0+6

              y=0+6

              y=6

x intercept is a point B(0,6).

What would be the angle for M

Answers

Answer:

180-124-33=23

Examine the following sequence 1, 4, 9, 16, 25…. Why is 36 the next number in the sequence? Because the pattern is:
a.
Add the next even number
c.
Cube the number of the term, n
b.
Square the number of the term, n
d.
Add 2 + the number of the term, n



Please select the best answer from the choices provided


A
B
C
D

Answers

Answer:36

Step-by-step explanation:it just is

LMNP is roatated 90 degrees clockwise around the origin

Answers

It would be c, (1, 0)

Answer:

C. L'(1, 0)

Step-by-step explanation:

Last question for the day plz help thank you!!<3

Answers

Answer: A

Step-by-step explanation:

What are the digits that repeat in the smallest sequence of repeating digits in the decimal equivalent of 2411?

Answers

Answer:

18

Step-by-step explanation:

.18 according to another Brainly answer with the same question

.
Find the y-intercept of y - x = 7.

Answers

Y= (0,7) is your answer

If i have 172 centimetres of ribbon to decorate a gift basket. How many more centimetres of ribbon would i need to make 3 metres

Answers

you would need 128 more centimeters of ribbon in order to make 3 meters worth of ribbon.

1 meter = 100 centimeters
3 meters = 300 centimeters
subtract 300 by 172
= 128 more centimeters

cosec 45^0
= ______ .​

Answers

Answer:

cosec45° = [tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the identity

cosec x = [tex]\frac{1}{sinx}[/tex] and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex]

Then

cosec45° = [tex]\frac{1}{\frac{1}{\sqrt{2} } }[/tex] = [tex]\sqrt{2}[/tex]

Name the ordered pair for the point

Answers

Answer:

the answer is 1,1 1/2 os c

Step-by-step explanation:

The lengths of the sides of the triangle are 13cm, 14 cm, and 15 cm. Is the triangle a right triangle?
Yes or No?

Show your work to receive brainliest! (lots of points)

Answers

Answer:

No, it is not a right triangle.

Step-by-step explanation:

If the triangle was a right triangle, then the Pythagorean Theorem states that a^2 + b^2 = c^2. Let's test it on this triangle:

13^2 + 14^2 = 365, or c^2. If this is a right triangle, c should equal 15.

However, sqrt(365) = 19.1, which is not 15. So, the triangle is not a right triangle.

The circle graph below shows the results of a survey about the number of TV's in a household. If you surveyed 250 households, how many would you predict to have 3 TV's?

Answers

Answer: answer

Step-by-step explanation: joe nuts

Y=52(0.42)^x identify if it's growth or decay and determine the percentage rate of increase or decrease

Answers

Answer:

58%

Step-by-step explanation:

Given the exponential relation :

Y=52(0.42)^x

Since 0.42 is less than 1, then we can infer that the expression is a Decay function ;

. General form of a exponential function :

y = A(1 - r)^x ; r = Decay rate

Comparing the general equation with the equation given ;

The percentage rate of decrease is obtained thus :

1 - r = 0.42

1 - 0.42 = r

r = 0.58

Rate = 0.58 * 100%

Rate = 58%

what does it mean to evaluate an expression in 5th grade

Answers

Answer:

Usually it means to solve it. Sometimes they give you values to substitute in for variables (letters) in the math sentence/equation/expression.

Does that make sense?

Step-by-step explanation:

What angle is paired with angle D as an alternate interior angle?

Answers

Answer:

E

Step-by-step explanation:

i dont know at this point

Answer:

angle E

Step-by-step explanation:

Hello There!

We need to find an angle that is a pair with angle D and they have to be alternate interior angles

alternate interior angle properties:

On the inside of the parallel linescongruent

In the image below; represents a pair of alternate interior angles

These properties match angle D with angle E

Why? they are both on the inside of the parallels

They also happen to be congruent

A right triangle has one leg of length y and hypotenuse of length x. What is the length of the other leg of this triangle
a x+y−−−−√
b x2+y2−−−−−−√
c x−y−−−−√
d x2−y2−−−−−−√

Answers

Answer:

Step-by-step explanation:

YALL HELP!!! it’s about reflection across the x axis

Answers

It might be A but I’m not totally sure
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