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In the equation ax^2 + bx + c = 0 a, b, and c are constants,

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In the equation ax^2 + bx + c = 0 a, b, and c are constants,  [#permalink]

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New post Updated on: 06 Mar 2013, 01:44
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In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 8a then which of the following is c equal to?

A. a/12
B. a/8
C. 6a
D. 8a
E. 12a

Originally posted by alex1233 on 05 Mar 2013, 11:32.
Last edited by Bunuel on 06 Mar 2013, 01:44, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In the equation ax^2 + bx + c = 0  [#permalink]

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New post 05 Mar 2013, 12:57
8a=b a=1 to make things simple
x^2+8x+c=0
given one of the roots are -2 we can factor and find the other root (x+2)(x+6)
c=12
c/a=12/1
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Re: In the equation ax^2 + bx + c = 0  [#permalink]

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New post 05 Mar 2013, 22:03
alexpavlos wrote:
In the equation \(ax^2 + bx + c = 0\) a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 8a then which of the following is c equal to?

a) a/12
b) a/8
c) 6a
d) 8a
e) 12a


The sum of the roots is = -b/a = -8a/a = -8. Let the other root be x. Thus, x-2 = -8

x = -6. Again, the product of the roots is -2*-6 = 12. Thus, c/a = 12. c = 12a.

E.
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Re: In the equation ax^2 + bx + c = 0 a, b, and c are constants,  [#permalink]

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New post 06 Mar 2013, 02:09
3
alexpavlos wrote:
In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 8a then which of the following is c equal to?

A. a/12
B. a/8
C. 6a
D. 8a
E. 12a


Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).


Thus according to the above \(x_1+x_2=-2+x_2=\frac{-b}{a}=\frac{-8a}{a}=-8\) --> \(x_2=-6\).

Also, \(x_1*x_2=-2*(-6)=\frac{c}{a}\) --> \(c=12a\).

Answer: E.

Similar questions testing this concept:
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if-f-x-5x-2-and-g-x-x-2-12x-85-what-is-the-sum-of-all-85989.html
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john-and-jane-started-solving-a-quadratic-equation-john-mad-106597.html

Hope it helps.
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Re: In the equation ax^2 + bx + c = 0 a, b, and c are constants,  [#permalink]

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New post 14 Jul 2018, 19:40
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alex1233 wrote:
In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 8a then which of the following is c equal to?

A. a/12
B. a/8
C. 6a
D. 8a
E. 12a


We can substitute -2 for x and 8a for b to solve for c:

a(-2)^2 + (8a)(-2) + c = 0

4a - 16a + c = 0

-12a + c = 0

c = 12a

Answer: E
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Re: In the equation ax^2 + bx + c = 0 a, b, and c are constants,   [#permalink] 14 Jul 2018, 19:40
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