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

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Question

Here  $p ( x )= kx ^{2}-\sqrt{2} x +1$ and $g ( x )= x -1$

$	herefore$ For $( x -1)$ be a factor of $p ( x ), p (1)$ should be equal to

Vedclass · Accepted Answer

$\sqrt{2}-1$

Vedclass · Answer

Here  $p ( x )= kx ^{2}-\sqrt{2} x +1$ and $g ( x )= x -1$

$	herefore$ For $( x -1)$ be a factor of $p ( x ), p (1)$ should be equal to $0 .$

since $\quad p (1)= k (1)^{2}-\sqrt{2}(1)+1 \quad$ or $p (1)= k -\sqrt{2}+1$

or $\quad \quad p(1)=k-\sqrt{2}+1 \quad 	herefore k-\sqrt{2}+1=0$

$\Rightarrow \quad k =\sqrt{2}-1$

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

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