Question

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

 

Answer 1

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" ."`