Question

Find the value of k, if x − 1 is a factor of x² + x + k.

Answer 1

Let f(x) = x² + x + k.
Since x − 1 is a factor of f(x), therefore
$$\begin{gathered} f\left(1\right)=0 \\ \Rightarrow 1^2+1+k=0 \\ \Rightarrow k=-2 \end{gathered}$$
Hence, k = − 2.