1962 AMC 12 Problem 21

Attempt Problem 21 of the 1962 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 1962 AMC 12 solutions, or check the answer key.

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

21.

It is given that one root of

2x^2+rx+s=0,

with

r

and

s

real numbers, is

3+2i

(i=\sqrt{-1}).

The value of

s

is:

undetermined

5

6

-13

26

A polynomial with real coefficients also has the conjugate root

Use the product of the roots and Vieta’s formula

The other root is

3-2i.

Their product is

(3+2i)(3-2i)=9+4=13.

Vieta’s formula gives

\frac{s}{2}=13,

s=26.

Therefore, the correct answer is E.

Problem 21 in other years