1963 AMC 12 Problem 14

Attempt Problem 14 of the 1963 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 1963 AMC 12 solutions, or check the answer key.

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

14.

Given the equations

x^2+kx+6=0

and

x^2-kx+6=0.

If, when the roots of the equations are suitably listed, each root of the second equation is

5

more than the corresponding root of the first equation, then

k

equals:

5

-5

7

-7

none of these

Compare the sums of the two pairs of roots

Adding

5

to each root increases their sum by

10

The first pair of roots has sum

-k,

while the second has sum

k.

Since both roots increase by

5,

k=-k+10,

k=5.

Therefore, the correct answer is A.

Problem 14 in other years