1964 AMC 12 Problem 7

Attempt Problem 7 of the 1964 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1964 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Let

n

be the number of real values of

p

for which the roots of

x^2-px+p=0

are equal. Then

n

equals:

0

1

2

a finite number greater than

2

an infinitely large number

Equal roots make the discriminant zero

Solve

p^2-4p=0

Equal roots require

(-p)^2-4p=p(p-4)=0.

Thus

p=0

p=4,

giving two real values.

Therefore, the correct answer is C.

Problem 7 in other years