1950 AMC 12 Problem 13

Attempt Problem 13 of the 1950 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 1950 AMC 12 solutions, or check the answer key.

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

13.

The roots of

(x^2-3x+2)(x)(x-4)=0

are:

4

0

and

4

1

and

2

0,

1,

2,

and

4

1,

2,

and

4

Factor the quadratic factor

A product is zero when at least one of its factors is zero

Since

x^2-3x+2=(x-1)(x-2),

the equation becomes

(x-1)(x-2)x(x-4)=0.

Its roots are

0,

1,

2,

and

4.

Thus, the correct answer is D.

Problem 13 in other years