2007 iTest Problems/Problem 18

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Problem

Suppose that $x^3+px^2+qx+r$ is a cubic with a double root at $a$ and another root at b, where $a$ and $b$ are real numbers. If $p=-6$ and $q=9$, what is $r$?

$\text{(A) }0\qquad \text{(B) }4\qquad \text{(C) }108\qquad \text{(D) It could be }0 \text{ or } 4\qquad \text{(E) It could be }0 \text{ or } 108 \$ (Error compiling LaTeX. ! Missing $ inserted.)

$\text{(F) }18\qquad \text{(G) }-4\qquad \text{(H) }-108\qquad \text{(I) It could be } 0 \text{ or } -4 \$ (Error compiling LaTeX. ! Missing $ inserted.)

$\text{(J) It could be } 0 \text{ or } {-108} \qquad \text{(K) It could be } 4 \text{ or } {-4}\qquad \text{(L) There is no such value of } r\qquad \$ (Error compiling LaTeX. ! Missing $ inserted.)

$\text{(M) } 1 \qquad \text{(N) } {-2} \qquad \text{(O) It could be } 4 \text{ or } -4 \qquad \text{(P) It could be } 0 \text{ or } -2 \qquad \$ (Error compiling LaTeX. ! Missing $ inserted.)

$\text{(Q) It could be } 2007 \text{ or a yippy dog} \qquad \text{(R) } 2007 \$ (Error compiling LaTeX. ! Missing $ inserted.)

Solution

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