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Find the value of k, if x – 1 is a factor of p(x) in the following case:- `p(x) = kx^2 - sqrt2x +1`

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#### Solution

If *x* − 1 is a factor of polynomial *p*(*x*), then *p*(1) must be 0.

`p(x) = kx^2 - sqrt2x +1`

*p*(1) = 0

`⇒ k(1)^2 - sqrt2(1) + 1 = 0`

`⇒ k - sqrt2 + 1`

`⇒ k = sqrt2 - 1`

Therefore, the value of k is `sqrt2 -1" ."`

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