A quadratic equation x²+2(3x+p)=0 where p is a constant, has roots a and 2a, where a≠0
(a) find the value of a and of p
(b) hence, from a quadratic equation whose roots are a+1 and a-5


HELP ME PLISS​

Answers

Answer 1

Answer:

a = -2 and p = 4.

Step-by-step explanation:

x²+2(3x+p)=0

x^2 + 6x + 2p = 0

For the general equation ax^2 + bx + c = 0, the sum of roots = -b/a and their product = c / a.

So here we have:

Sum of the roots:

a + 2a = -6/1 = -6

Product of the roots = 2a^2 = 2p/1 = 2p..

So 3a = -6 and

a = -2.

and

2(-2)^2 = 2p

8 = 2p

p = (-2)^2 = 4.

Answer 2

Answer:

see explanation

Step-by-step explanation:

Since x = a and x = 2a are roots, then substitute these values into the equation.

x = a

a² + 2(3a + p) = 0, that is

a² + 6a + 2p = 0 → (1)

x = 2a

(2a)² + 2(3(2a) + p) = 0

4a² + 12a + 2p = 0 → (2)

Solving simultaneously

Subtract (1) from (2) term by term to eliminate p

3a² + 6a = 0 ← in standard form

3a(a + 2) = 0 ← in factored form

Equate each factor to zero and solve for a

3a = 0 ⇒ a = 0

a + 2 = 0 ⇒ a = - 2

Since a ≠ 0 then a = - 2

Substitute a = - 2 into either of the 2 equations and solve for p

substituting into (1)

(- 2)² + 6(- 2) + 2p = 0

4 - 12 + 2p = 0

- 8 + 2p = 0 ( add 8 to both sides )

2p = 8 ( divide both sides by 2 )

p = 4

Thus a = - 2 and p = 4

--------------------------------------------

a + 1 = - 2 + 1 = - 1

a - 5 = - 2 - 5 = - 7

If x = - 1 and x = - 7 are roots then the corresponding factors are

(x + 1) and (x + 7) and the quadratic equation is the product of the factors, that is

(x + 1)(x + 7) = 0 ← expand left side using FOIL

x² + 8x + 7 = 0


Related Questions

V = BH - 5
How do I solve for b in this equation

Answers

Answer:

[tex]B=\frac{V+5}{H}[/tex]

Step-by-step explanation:

Add 5 to both sides:

V+5=BH

Divide both sides by H:

[tex]B=\frac{V+5}{H}[/tex]

Write an equation in slope-intercept form of the line with slope −4/5 that contains the point (−5,−4)

.

y=−45x−5

y=−4/5x−8

y=−4/5x−4

y=−4/5x+4

Answers

Our point is (-5, -4)

Now use point slope form to find the equation: (y - y1) = m(x - x1)

(y - y1) = m(x - x1)

(y - (-4)) =-4/5(x - (-5))

y + 4 = -4/5x +4

An equation in slope-intercept form of the line is y = -4/5x - 8. The correct option is B.

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the slope −4/5 contains the point (−5,−4). The equation of the line is written as,

y = mx + c

-4 = -4/5 x - 5 + c

-4 = 4 + c

c = -8

The equation will be written as,

y = -4/5x - 8

To know more about an equation of the line follow

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What type of number can √134 be classified as?

A) irrational number
B) Rational number
C) integer
D) whole number

What type of number is 0 classified as?

A) Irrational number
B) Whole number
C) Integer

Answers

Answer:

[tex] \sqrt{134 } = irrational \\ 0 = whole \: no. \: and \: integer. \\ hope \: it \: helps \\ plzz \: mark \: as \: brainliest....[/tex]

:-)

HELP ME!!!!!!!! Which choice represents the fraction below as a single exponential expression? This is unit is The Division Law of Exponents.

Answers

The answer is C. 5^4

2 w = 2p - 3z
a Find w when p = 8 and z = -2

Answers

Answer:

11

Step-by-step explanation:

2w = 2×8 - (-2×3)

2w = 16 - (-6)

2w = 22

w = 11

What is the equation of the top line graphed below?

Answers

Answer:

I think it has to y=mx+b

Step-by-step explanation:

Nikki Grows 20 Tomato plants. She measures their heights to the nearest centimetre, and writes them down

Answers

Answer:

ok? what am i supposed to do

Step-by-step explanation:

Answer:

The answers are 2, 6, 10, 2.

Step-by-step explanation:

Mariah025 answer here please

Answers

Answer:

wht

!?

............

..............

..

.

Answer the following Question with Appropriate Explanation

Answers

Answer:

option is B)

Step-by-step explanation:

2x is a perfect square. but x is not a perfect square, this brings us to the conclusion tht prob x is 2.

2x = 4

hence correct option is B) 4x is a perfect square, as 4x4=16, which is a perfect square...

Ellie bought a pair of jeans on sale for 15% off. If the jeans were originally $35, how much did she save?

Answers

Answer:5.25

Step-by-step explanation:

1) Choose the correct answer.


The ___ of two sets is the set of elements that could be found in both sets at the same time.

intersection

union

conjunction

disjunction

Answers

Answer:

Intersection

Step-by-step explanation:

The intersection of two set A and B is defined as the elements which can be found in both set A and set B.

For instance :

A = {1, 3, 5, 7, 9, 11}

B = {2, 4, 6, 7, 8, 9, 10}

The intersection of the two sets A and B denoted as ;

AnB = {7, 9}

what is 1/2x + 8 < -4 ?

Answers

Answer:

-1/24 < x < 0

Step-by-step explanation:

1/2x + 8 must be less than -4 therefore x can only be x<-24

function or not a function?

Answers

Answer:

not a function

Step-by-step explanation:

there are two of the same inputs 4 and 4 that will cause it to not be a function

At a local fair, Molly sells bracelets. It costs her
$10 per bracelet for supplies and the local marke
charges her a one-time booth fee of $60. She
charges $20 for each bracelet.
a) Write a system of equations to represent this
situation (one equation for expenses and one
equation for income):

Answers

Answer:

10x + 60 ; 20x

Step-by-step explanation:

Given that:

Purchase price per bracelet = $10

Cost of booth = $60

Selling price per bracelet = $20

Hence,

Let number of bracelets = x

Expense equation :

(Price per bracelet * number of bracelet) + booth fee

(10 * x) + 60

10x + 60

Income equation :

Selling price * number of bracelets

20x

Which expression is equivalent to sqrt 2x^5/18 assume x is greater than or equal to 0

Answers

Answer:

  [tex]\sqrt{\frac{2x^{5} }{18} }[/tex]   = [tex]\frac{\sqrt{x^{5} } }{3}[/tex]

Step-by-step explanation:

Given expression

            [tex]\sqrt{\frac{2x^{5} }{18} }[/tex]

we know that the algebra formula

[tex]\sqrt{\frac{a}{b} } = \frac{\sqrt{a} }{\sqrt{b} }[/tex]

[tex]\sqrt{\frac{2x^{5} }{18} } = \frac{\sqrt{2} \sqrt{x^{5} } }{\sqrt{18} } = \frac{\sqrt{2} \sqrt{x^{5} } }{\sqrt{9} \sqrt{2} }[/tex]

          = [tex]\frac{\sqrt{x^{5} } }{3}[/tex]

Find the missing side length, N. ​

Answers

Answer : 15

We know these triangles are congruent. To find the missing side, you first have to find out what the scale factor is. To do this you can just divide side QS by side AC, which would give you 2.5.
You would then multiply this scale factor by side BC, giving you side N, which is 15.

We know these triangles are congruent with the missing side, N would be equal to 15.

What is the congruent triangle?

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We know these triangles are congruent.

To find the missing side, N

ΔABC ≅ΔQRS

AC/QS = BC/RS

2/5 = 6/n

n = 6 x 5/2

n = 30/2

n = 15

Thus, the value of N is 15.

Learn more about triangles;

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Please help. I need to refresh my mind of this problem and a few more if you don't mind

Answers

Answer: c

Step-by-step explanation:

look at the equation and insert the value of X from the table into the equation and figure out which one will give you the same sum for the values. for example f(x) = 3(-2)-1

this answer gives you f(x)= -6 -1 which will give u a sum of -7

another one : f(x)= 3(0)-1

3 multiplied by 0 gives you 0 therefore you are left with -1

by doing this you prove that this equation works with ur x values and gives you the same sum you have for f(x)

WILL GIVE BRAINLIEST!!!!!!!!!!
A sandcastle can be modeled with four 6-inch-tall square prisms, one on top of the other, as shown in the figure below.
The base of the bottom prism has a side length of 30 inches, and the base of each of the other three prisms has a side length 7 inches less than the side length of the base of the prism below it. What is the volume of the sand castle?

Answers

Answer:

A 2808

Step-by-step explanation:

From top to bottom

The top one is 9

Second layer is 16

Third is 23

Bottom is 30

I did 9 x 6, 16 x 6, 23 x 6, 30 x 6 = 54, 96, 138, 180

Added all of them up and got 468 then I times it by 6 and got 2808

Heyo! ;D

The volume of the sandcastle above is 10,596 cubic inches.

Hope this helped! If so, please lmk! Tysm and good luck!

Find the slope of the line that passes through A(0, -5) and B(3,-4)

Answers

Answer:

1/3

Step-by-step explanation:

(-4-(-5))/(3-0) = 1/3

delta math help plz im stuck

Answers

Step-by-step explanation:

-70x^4 + 30x

= 10x(-7x^3 + 3)

ANSWER: 10x(-7x^3 + 3)

Tim has m dollars. Rebecca has $6 less than times the number of dollars that Tim has. Which expression represents the total amount of money that Tim and Rebecca have? If Tim has $70, how much money do Rebecca and Tim have altogether?

Answers

Answer:

$71

Step-by-step explanation:

Tim has M dollars

Rebecca is having (M/10 - 6)

Then, the amount of money Tim and Rebecca are having

= M + M/10 - 6

= (11M/10) - 6 dollars

The expression representing the total amount of money is [(11X/10) - 6]

If Tim is having $70, then total amount both would have together

= [(11 × 70/10) - 6]

= 77 - 6

= $71

Therefore, the expression for the total amount is [(11M/10) - 6] dollars

The total amount both are having together is $71.

Answer:

B. The expression is 11/10m – 6, and the amount is $71.

Step-by-step explanation:

i'll mark brainliest just tell me how to.

Answers

Answer:

a = 12

b = 2

c = 11

Step-by-step explanation:

[tex] \frac{( {x}^{5}y {z}^{4} )^{3} }{ {x}^{3} yz} = {x}^{a} {y}^{b} {z}^{c} \\ \\ \frac{ {x}^{5 \times 3}y^{3} {z}^{4 \times 3} }{ {x}^{3} yz} = {x}^{a} {y}^{b} {z}^{c} \\ \\ \frac{ {x}^{15}y^{3} {z}^{12} }{ {x}^{3} yz} = {x}^{a} {y}^{b} {z}^{c} \\ \\ {x}^{15 - 3} {y}^{3 - 1} {z}^{12 - 1} = {x}^{a} {y}^{b} {z}^{c} \\ \\ {x}^{12} {y}^{2} {z}^{11} = {x}^{a} {y}^{b} {z}^{c} \\ \\ equating \: like \: terms \: from \: both \: sides \\ \\ {x}^{12} = {x}^{a} \: \implies \: a = \boxed{ 12}\\ \\ {y}^{2} = {y}^{b} \: \implies \: b = \boxed{ 2} \\ \\ {z}^{11} = {z}^{c} \: \implies \: c = \boxed{ 11}[/tex]

Start by finding the scale of this map. At the actual gym, one side length of the snack stand is 60 feet. On the scale map, it is 20 cm. What is the scale?

Answers

Answer:

I actual foot represents 0.01093 foot on paper

Step-by-step explanation:

Given that :

Actual side length of snack stand = 60 feets

Length of side on map = 20cm

Scaie :

60 feet = 20cm

1 foot = (20/60) cm

1 foot = 0.333 cm

1cm = 0.0328084 foot

0.333cm = (0.33 * 0.0328084) = 0.01093 feets

Scale :

I actual foot represents 0.01093 foot on paper

Write the equation of the line that passes through the given points.

(0,- 4) and (2,3)

The equation of the line is( )​

Answers

Answer:

[tex] \frac{y - ( - 4)}{x - 0} = \frac{3 - ( - 4)}{2 - 0} \\ \frac{y + 4}{x} = \frac{3 + 4}{2} \\ \frac{y + 4}{x} = \frac{7}{2} \\ 2(y + 4) = 7x \\ 7x = 2y + 8 \\ 7x - 2y = 8 \\ 2y = 7x - 8 \\ \boxed{y = \frac{7}{2}x - 4}[/tex]

y=(7/2)x-4 is the right answer.

Pls help and show workings

Answers

Step-by-step explanation:

AB = 72 so, then FB would be half of that

so 72 divided by 2 would be 36

5x+1=36 then do substitution

-1 from both sides (from +1 you gotta do the inverse)

5x = 35

divide 5 from both sides because in between 5 and x is a times so the inverse of that is divide

x = 7

Need help with these

Answers

Answer:

3x

7-k

m/4

(5x)+12

Step-by-step explanation:

most of the words like and are just fillers. and basically means together in this instance

6x + 57= 135 solve x​

Answers

Answer:

can't find answer sorry

The lines graphed below are perpendicular. The slope of the red line is
What is the slope of the green line?

Answers

Answer:

Is there a picture for this one and also you didn't mention the slope of the red line is?

Step-by-step explanation:

Answer:

The slope of the Green line should be the same as the red line- but a negative number instead of a positive.

Step-by-step explanation:

This is the inverse of the line

So by reflecting it over the y-axis, the slope remains the same but will change from positive to negative and vise versa

Peaches are being sold for $2 per pound.The customer created a model to represent the total cost of peaches bought. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y?

The values of both x and y can be any real number.
The values of both x and y will be real numbers greater than or equal to 0.
The value of x and y will always be zero
The value of x can be any real number greater than or equal to 0, but the value of y must be an integer greater than or equal to 0.

Answers

Answer:

B - The values of both x and y will be real numbers greater than or equal to 0.

The answer choice that best describes the values of x and y is B - The values of both x and y will be real numbers greater than or equal to 0.

Calculations and Parameters:

Given that peaches are being sold for $2 per lb.

If we define x as the number of pounds that you buy, and y as the cost of these peaches, we can write the function:

y = $2*x

Therefore, the best description of the values of x and y is found in option B. The value of x can be any real number greater than or equal to 0, but the value of y must be an integer greater than or equal to 0.

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What is the value of 7(4 + x) when x = 5?

Answers

Answer:

63

Step-by-step explanation:

7(4+x)

Distribute: 28 + 7x

Substitute: 28 + 7(5)

Simplify: 28 + 35

Simplify: 63

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