Question

The zeroes of the quadratic polynomial x² + x – 6 are __________.

Answer 1

Let f(x) = x² + x – 6

$$\begin{gathered} \Rightarrow f\left(x\right)=x^2+x-6 \\ =x^2+3x-2x-6 \\ =x\left(x+3\right)-2\left(x+3\right) \\ =\left(x-2\right)\left(x+3\right) \\ \mathrm{To}\mathrm{find}\mathrm{the}\mathrm{zeroes},\mathrm{we}\mathrm{put}f\left(x\right)=0 \\ \Rightarrow \left(x-2\right)\left(x+3\right) \\ \Rightarrow \left(x-2\right)=0\mathrm{or}\left(x+3\right)=0 \\ \Rightarrow x=2,-3 \end{gathered}$$

Hence, the zeroes of the quadratic polynomial x² + x – 6 are 2 and –3.