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The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts of the graph of $f$?
 

The polynomial \(f(x)\) has degree 3. If \(f(-1) = 15\), \(f(0)= 0\), \(f(1) = -5\), and \(f(2) = 12\), then what are the \(x\)-intercepts of the graph of \(f\)?

 

Please use Desmos for the graphs if possible.

 Mar 27, 2019
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\(f(x) = a x^3 + b x ^2 + c x + d\\ f(0) = 0 \Rightarrow d = 0\\ \begin{pmatrix}-1 &1 &-1 \\1 &1 &1 \\8 &4 &2\end{pmatrix}\begin{pmatrix}a\\b\\c\end{pmatrix}= \begin{pmatrix}15 \\-5 \\12\end{pmatrix}\)

 

\(\text{Use Gaussian elimination to obtain}\\ \begin{pmatrix}a\\b\\c\end{pmatrix} = \begin{pmatrix}2 \\5\\-12\end{pmatrix}\\ f(x) =2x^3 +5x^2 -12x\)

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 Mar 27, 2019

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