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# Find the value of k, if x - 1 is a factor of p(x) in the following case: (iv) kx ^2 - 3 x + k

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

(iv)    $p(x) = kx^2 -3 x + k$

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Zero of polynomial   $x - 1$ is  $1$

If  $x - 1$  is factor of polynomial   $p(x) = kx^2 -3 x + k$

Then,  $p(1)$  must be equal to zero

Now,

$\Rightarrow p(1) = k(1)^2 -3(1) + k$

$\Rightarrow p(1) =0$

$\Rightarrow k -3+k= 0$

$\Rightarrow k = \frac{3}{2}$
Therefore,  value of k is  $\frac{3}{2}$

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