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

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

(ii)    $p(x) = 2x^2 + kx + \sqrt2$

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Zero of polynomial   $x - 1$ is  $1$

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

Then,  $p(1)$  must be equal to zero

Now,

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

$\Rightarrow p(1) =0$

$\Rightarrow 2+k +\sqrt2= 0$

$\Rightarrow k = -(2+\sqrt2)$

Therefore,  value of k is $-(2+\sqrt2)$

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