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

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 = 8Also, if p is the only solution to the equation, then

p = 4So, h/p =

8/

4 = 2

Answer: D

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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