MathDB
Polynomial with 5 Intercepts

Source:

February 20, 2008
algebrapolynomialVieta

Problem Statement

The graph of the polynomial P(x) \equal{} x^5 \plus{} ax^4 \plus{} bx^3 \plus{} cx^2 \plus{} dx \plus{} e has five distinct x x-intercepts, one of which is at (0,0) (0,0). Which of the following coefficients cannot be zero?
<spanclass=latexbold>(A)</span> a<spanclass=latexbold>(B)</span> b<spanclass=latexbold>(C)</span> c<spanclass=latexbold>(D)</span> d<spanclass=latexbold>(E)</span> e <span class='latex-bold'>(A)</span>\ a \qquad <span class='latex-bold'>(B)</span>\ b \qquad <span class='latex-bold'>(C)</span>\ c \qquad <span class='latex-bold'>(D)</span>\ d \qquad <span class='latex-bold'>(E)</span>\ e