Question

Find the zeroes of the quadratic polynomials given below. Find the sum and product of the zeroes and verify relationship to the coefficients of the terms in the polynomials.
$p\left(x\right)=x^2-x-6$

Answer 1

$p\left(x\right)=x^2-x-6$

$=x^{}-3x+2x-6$

$=x(x-3)+2(x-3)$

$=(x-3)(x+2)$

$=(x-3)(x+2)$

$\therefore$ The value of p(x) is zero when $x=3$ or $x=-2$

$\therefore$ Sum of the Zeroes $=3-2=1$ $=-\frac{-1}{1}=\frac{coefficientofx}{coefficientof{x}^2}=-\frac{b}{a}$

$\therefore$ Product of zeroes $=3\times (-2)=-6=\frac{-6}{1}=\frac{c}{a}$