Question

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

p(x) = ${\displaystyle 2x^2+kx+\sqrt{2}}$

Answer 1

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

p(x) = ${\displaystyle 2x^2+kx+\sqrt{2}}$

p(1) = 0

⇒ ${\displaystyle 2{\left(1\right)}^2+k\left(1\right)+\sqrt{2}=0}$

⇒ ${\displaystyle 2+k+\sqrt{2}=0}$

⇒ k = ${\displaystyle -2-\sqrt{2}}$

k = ${\displaystyle -(2+\sqrt{2})}$

Therefore, the value of k is ${\displaystyle -(2+\sqrt{2})}$.