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GRE Math Challenge #46-If h > 0 and p is the only
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19 Sep 2014, 03:51
19 Sep 2014, 03:51
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Question Stats:
58% (01:36) correct
41% (01:56) wrong based on 55 sessions
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If \(h > 0\) and p is the only value of x for which eq: \(x^2 - h *x +16 = 0\), then \(\frac{h}{p}\) =
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
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Posts: 6218
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Re: GRE Math Challenge #46-If h > 0 and p is the only
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03 Dec 2018, 10:53
03 Dec 2018, 10:53
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sandy wrote:
If \(h > 0\) and p is the only value of x for which eq: \(x^2 - h *x +16 = 0\), then \(\frac{h}{p}\) =
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
IMPORTANT HINT: When we read that the quadratic equation x² - hx + 16 = 0 has only 1 solution, our reaction should be "Hmmm, that's odd; quadratic equations usually have 2 solutions.
For example, the equation x² - 5x + 6 = 0 can be rewritten as (x - 3)(x - 2) = 0, which means the two solutions are x = 3 and x = 2
That said, there ARE times when a quadratic equation has 1 solution.
This occurs when the quadratic expression can be factored into a binomial times itself.
For example, the equation x² - 6x + 9 = 0 can be rewritten as (x - 3)(x - 3) = 0, which means there's exactly one solution: x = 3
From here, we might recognize that the equation x² - 8x + 16 = 0 can be rewritten as: (x - 4)(x - 4) = 0, which means there's exactly one solution: are x = 4
In the question, we're given the equation x² - hx + 16 = 0
Since the equation x² - 8x + 16 = 0 has ONE solution, we can conclude that h = 8
Also, if p is the only solution to the equation, then p = 4
So, h/p = 8/4 = 2
Answer: D
Cheers,
Brent
Re: GRE Math Challenge #46-If h > 0 and p is the only
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05 Jun 2021, 04:54
05 Jun 2021, 04:54
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