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2002 AMC 10A Problem 10

Problem 10 of 25EasierAlgebra

Compute the sum of all the roots of (2x+3)(x−4)(2x+3)(x-4) +(2x+3)(x−6)=0.+(2x+3)(x-6)=0.

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Solution

Factoring, (2x+3)[(x−4)+(x−6)]=(2x+3)(2x−10)=0. \begin{gathered} (2x+3)\left[(x-4)+(x-6)\right] \\ = (2x+3)(2x-10) \\ = 0. \end{gathered} The roots are −32-\dfrac{3}{2} and 5,5, which sum to 72.\dfrac{7}{2}. Thus, the correct answer is A.
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Tagged: quadratic · factoring

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