If $x+1$ is a factor of $2x^3 + ax^2 + 2bx + 1$ then find the values of $a$ and $b$, given that $2a - 3b = 4$.
If $x+1$ is a factor of $2x^3 + ax^2 + 2bx + 1$ then find the values of $a$ and $b$, given that $2a - 3b = 4$.
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geometry
polynomials
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1Please pick a descriptive question title, in the future. – 2012-09-23
1 Answers
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$(x+1)\mid (2x^3+ax^2+2bx+1)\Longleftrightarrow 2(-1)^3+a(-1)^2+2b(-1)+1=0$
So we get the following linear system in the unknowns $\,a,b\,$ :
$\begin{align*}a-2b&=1\\2a-3b&=4\end{align*}$
Can you take it from here?
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0Don't worry, @aayush: we all do those things at the beginning. – 2012-09-23