Question
Write the zeros of the polynomial $x^2 - x - 6.$
✓
Answer
$f(x) = x^2 - x - 6$
$= x^2 - 3x + 2x - 6$
$\begin{Bmatrix}-6=-3\times2\\-1=-3+2\end{Bmatrix}$
$= x(x - 3) + 2(x - 3)$
$= (x - 3)(x + 2)$
$\therefore$ Zeros of $f(x)$ will be if $(x - 3)(x + 2) = 0$
Either $x - 3 = 0,$ then $x = 3$
$or x + 2 = 0$, then $x = 3$
$\therefore$ Zeros are $3, -2$
$= x^2 - 3x + 2x - 6$
$\begin{Bmatrix}-6=-3\times2\\-1=-3+2\end{Bmatrix}$
$= x(x - 3) + 2(x - 3)$
$= (x - 3)(x + 2)$
$\therefore$ Zeros of $f(x)$ will be if $(x - 3)(x + 2) = 0$
Either $x - 3 = 0,$ then $x = 3$
$or x + 2 = 0$, then $x = 3$
$\therefore$ Zeros are $3, -2$
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