Difference between revisions of "2018 AMC 12A Problems/Problem 5"

Revision as of 17:25, 8 February 2018

Problem

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?

$\textbf{(A) }3 \qquad\textbf{(B) }4 \qquad\textbf{(C) }5 \qquad\textbf{(D) }6 \qquad\textbf{(E) }10 \qquad$

Solution

We factor $x^2-3x+2$ into $(x-1)(x-2)$ . Thus, either $1$ or $2$ is a root of $x^2-5x+k$ . If $1$ is a root, then $1^2-5\cdot1+k=0$ , so $k=4$ . If $2$ is a root, then $2^2-5\cdot2+k=0$ , so $k=6$ . The sum of all possible values of $k$ is $\boxed{\textbf{(E)}10}$ .

2018 AMC 12A (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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 ==See Also==
-{{AMC12 box|year=2018|ab=A|before=First Problem|num-a=2}}
+{{AMC12 box|year=2018|ab=A|num-b=4|num-a=6}}
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Difference between revisions of "2018 AMC 12A Problems/Problem 5"

Revision as of 17:25, 8 February 2018

Problem

Solution

See Also