Question

Find the value of k, if (x −1) is a factor of p(x) in each of the following cases:
$\left(i\right)p\left(x\right)=x^2+x+k$
$\left(ii\right)p\left(x\right)={2x}^2+kx+\sqrt{2}$ [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark each
Solution: 0.5 Mark each

$\left(i\right)p\left(x\right)=x^2+x+k$

$p\left(1\right)=0$ (Using Remainder Theorem)

$p\left(1\right)=1^2+1+k=0$

$1+1+k=0$

$k=-2$

$\left(ii\right)p\left(x\right)={2x}^2+kx+\sqrt{2}$

$p\left(1\right)=0$ (Using Remainder Theorem)

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

$2+k+\sqrt{2}=0$

$k=-2-\sqrt{2}$