1958 AMC 12 Problem 10

Attempt Problem 10 of the 1958 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 1958 AMC 12 solutions, or check the answer key.

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

10.

For what real values of

k,

other than

k=0,

does the equation

x^2+kx+k^2=0

have real roots?

k\lt0

k\gt0

k\ge1

all values of

k

no values of

k

Use the discriminant condition for a quadratic to have real roots

Compute

k^2-4k^2

and use the restriction

k\ne0

The discriminant is

k^2-4k^2=-3k^2.

For every nonzero real

k,

this is negative, so the quadratic has no real roots.

Thus, the correct answer is E.

Problem 10 in other years