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# GRE Math Challenge #52- equation x^2 + ax - b = 0 has

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Joined: 16 May 2014
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GRE Math Challenge #52- equation x^2 + ax - b = 0 has [#permalink]  28 Feb 2015, 02:14
Expert's post
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Question Stats:

69% (00:28) correct 30% (02:55) wrong based on 13 sessions
The equation $$x^2 + ax - b = 0$$ has equal roots, and one of the roots of the equation $$x^2 +ax + 15 = 0$$ is 3. What is the value of b?

A. -64
B. -16
C. -15
D. -1/16
E. -1/64
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #52 [#permalink]  05 May 2015, 23:34
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Re: GRE Math Challenge #52- equation x^2 + ax - b = 0 has [#permalink]  16 Feb 2017, 00:49
The answer is B.(-16).
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Re: GRE Math Challenge #52- equation x^2 + ax - b = 0 has [#permalink]  03 Apr 2019, 02:21
how is the answer C? can someone please explain?
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Re: GRE Math Challenge #52- equation x^2 + ax - b = 0 has [#permalink]  03 Apr 2019, 03:31
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Expert's post
I believe the answer should be B.

First, we know that 3 is a root of the second equation. So when x = 3, the equation should be valid. Hence:

$$3^{2}+a3 +15= 0$$

$$3a + 24 = 0$$

$$3a = -24$$

$$a = -8$$

Now we plug that into our second equation:

$$x^{2}-8x - b = 0$$

Since we know this equation has equal roots, it must be true that (x - r)(x - r) = 0 for some r must be true. Since our middle term is -8, r must equal 4. Hence, our factorization is:

$$(x - 4)(x - 4) = x^{2}- 8x + 16 = 0$$

We see that our final term here is 16. This means b = -16.
Re: GRE Math Challenge #52- equation x^2 + ax - b = 0 has   [#permalink] 03 Apr 2019, 03:31
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# GRE Math Challenge #52- equation x^2 + ax - b = 0 has

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