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# Find the value of k, if x - 1 is a factor of p(x) in the following case: (iii) kx ^2 - root 2 x + 1

3.(iii)  Find the value of k, if $x - 1$ is a factor of p(x) in the following case:

(iii)    $p(x) = kx^2-\sqrt2 x + 1$

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Zero of polynomial   $x - 1$ is  $1$

If  $x - 1$  is factor of polynomial   $p(x) = kx^2-\sqrt2 x + 1$

Then,  $p(1)$  must be equal to zero

Now,

$\Rightarrow p(1) = k(1)^2 -\sqrt2(1) + 1$

$\Rightarrow p(1) =0$

$\Rightarrow k -\sqrt2 +1= 0$

$\Rightarrow k = -1+\sqrt2$

Therefore,  value of k is $-1+\sqrt2$

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