Question

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

`p(x) = 2x^2+kx+sqrt2`

 

Answer 1

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

`p(x) = 2x^2+kx+sqrt2`

p(1) = 0

`⇒ 2(1)^2 + k(1) + sqrt2 = 0`

`⇒ 2 + k + sqrt2 = 0`

`⇒ k = -2 -sqrt2 = -(2+sqrt2)`

Therefore, the value of k is `-(2+sqrt2)" ."`