Find the value of k, if x -1 is a factor of p | vedclass

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Question

Here $p ( x )=2 x ^{2}+ kx +\sqrt{2}$

For $x-1$ be a factor of $p(x), \,p(1)=0$.

Since,    $p (1)=2(1)^{2}+ k (1)+\sqrt{2}=2+ k +\sqrt

Vedclass · Accepted Answer

$k =-2-\sqrt{2}$

Vedclass · Answer

Here $p ( x )=2 x ^{2}+ kx +\sqrt{2}$

For $x-1$ be a factor of $p(x), \,p(1)=0$.

Since,    $p (1)=2(1)^{2}+ k (1)+\sqrt{2}=2+ k +\sqrt{2}$

$\because p (1)$ must be equal to $0 .$

$	herefore  k+2+\sqrt{2} =0 $                        $\Rightarrow k =-2-\sqrt{2}$

 or   $k=-(2+\sqrt{2}) $ .

Find the value of $k$, if $x -1$ is a factor of $p(x)$ in this case : $p(x)=2 x^{2}+k x+\sqrt{2}$

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