2018 AMC 12A Problem 5

Problem 5 of 25EasierAlgebra

What is the sum of all possible values of

k

for which the polynomials

x^2 - 3x + 2

and

x^2 - 5x + k

have a root in common?

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Solution

Since

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

its roots are

1

and

2.

1

is a shared root then

1 - 5 + k = 0,

k = 4.

2

is a shared root then

4 - 10 + k = 0,

k = 6.

The sum of possible values is

4 + 6 = 10.

Thus, the correct answer is E.

Concepts: quadratic · factoring

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