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2007 iTest Problems/Problem 18: Difference between revisions

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Suppose that <math>x^3+px^2+qx+r</math> is a cubic with a double root at <math>a</math> and another root at b, where <math>a</math> and <math>b</math> are real numbers.
Suppose that <math>x^3+px^2+qx+r</math> is a cubic with a double root at <math>a</math> and another root at b, where <math>a</math> and <math>b</math> are real numbers.
If <math>p=-6</math> and <math>q=9</math>, what is <math>r</math>?
If <math>p=-6</math> and <math>q=9</math>, what is <math>r</math>?
<math>\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 \\ </math>
<math>\text{(F) }18\qquad
\text{(G) }-4\qquad
\text{(H) }-108\qquad
\text{(I) It could be } 0 \text{ or } -4 \\ </math>
<math>\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 \\ </math>
<math>\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 \\ </math>
<math>\text{(Q)  It could be } 2007 \text{ or a yippy dog} \qquad
\text{(R)  } 2007 \\ </math>


== Solution  ==
== Solution  ==

Revision as of 16:16, 1 January 2017

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 $r$?

Solution

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