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

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Intern
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In the equation ax^2 + bx + c = 0 a, b, and c are constants, [#permalink]  05 Mar 2013, 10:32
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Mar 2013, 00:44, edited 1 time in total.
Renamed the topic and edited the question.
Intern
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Re: In the equation ax^2 + bx + c = 0 [#permalink]  05 Mar 2013, 11:57
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]  05 Mar 2013, 21:03
Expert's post
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]  06 Mar 2013, 01:09
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Expert's post
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, $$x_1*x_2=-2*(-6)=\frac{c}{a}$$ --> $$c=12a$$.

Similar questions testing this concept:
if-q-is-one-root-of-the-equation-x-2-18x-11c-0-where-141199.html
if-f-x-5x-2-and-g-x-x-2-12x-85-what-is-the-sum-of-all-85989.html
if-4-is-one-solution-of-the-equation-x2-3x-k-10-where-139119.html

Hope it helps.
_________________
Re: In the equation ax^2 + bx + c = 0 a, b, and c are constants,   [#permalink] 06 Mar 2013, 01:09
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