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# help pls

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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

### 1+0 Answers

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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