Question

If –4 is a zero of the polynomial x² – x – (2k + 2), then k = _________.

Answer 1

Let f(x) = x² – x – (2k + 2)

It is given that –4 is a zero of f(x).

Therefore, $f\left(x\right)=0\mathrm{when}x=-4$.

On putting x = –4 in f(x) = 0, we get

$$\begin{gathered} {\left(-4\right)}^2-\left(-4\right)-\left(2k+2\right)=0 \\ \Rightarrow 16+4-2k-2=0 \\ \Rightarrow 20-2k-2=0 \\ \Rightarrow 18-2k=0 \\ \Rightarrow 2k=18 \\ \Rightarrow k=9 \end{gathered}$$

Hence, if –4 is a zero of the polynomial x² – x – (2k + 2), then k = 9.