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A polynomial in x of third …

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A polynomial in x of third degree which will vanish when x=1 & x=-2 and will have the values 4 & 28 when x=-1 and x=2 respectively is_______.

Posted by Sudhanshu Baranwal 6 years, 9 months ago

CBSE > Class 11 > Mathematics

1 answers

Sunil C N 6 years, 8 months ago

equation is{tex} ax^3+bx^2+cx+d{/tex}

when x=1

{tex} a+b+c+d=0{/tex} when {tex} x=1{/tex}

{tex} -8a+4b-2c+d=0{/tex} when {tex} x=-2{/tex}

{tex} -a+b-c+d=4{/tex} when {tex} x=-1{/tex}

{tex} 8a+4b+2c+d=28{/tex} when {tex} x=2{/tex}

{tex}\begin{pmatrix} 1 & 1 & 1 & 1 \\ -8 & 4 & -2 & 1 \\ -1 & 1 & -1& 1\\ 8 & 4 &2 & 1\end{pmatrix} \ \begin{pmatrix} a \\ b \\ c\\ d\end{pmatrix} \ =\begin{pmatrix} 0 \\ 0 \\ 4\\ 28\end{pmatrix} \ {/tex}

<pre> {tex} \begin{pmatrix} a \\ b \\ c\\ d\end{pmatrix} \ =inverse\begin{pmatrix} 1 & 1 & 1 & 1 \\ -8 & 4 & -2 & 1 \\ -1 & 1 & -1& 1\\ 8 & 4 &2 & 1\end{pmatrix}\begin{pmatrix} 0 \\ 0 \\ 4\\ 28\end{pmatrix} \ {/tex} </pre>

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