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Polynomial Remainders

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December 31, 2005
algebrapolynomialquadraticsRational Root Theorem

Problem Statement

For some real number rr, the polynomial 8x3−4x2−42x+458x^3-4x^2-42x+45 is divisible by (x−r)2(x-r)^2. Which of the following numbers is closest to rr? (A) 1.22(B) 1.32(C) 1.42(D) 1.52(E) 1.62\text{(A)} \ 1.22 \qquad \text{(B)} \ 1.32 \qquad \text{(C)} \ 1.42 \qquad \text{(D)} \ 1.52 \qquad \text{(E)} \ 1.62
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