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`

k = `-(2+sqrt2)`

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