Question

Verify that
(i) 1 and 2 are the zeros of the polynomial, $p\left(x\right)=x^2-3x+2$.
(ii) 2 and -3 are the zeros of the polynomial, $q\left(x\right)=x^2+x-6.$
(iii) 0 and 3 are the zeros of the polynomial, $r\left(x\right)=x^2-3x$.

Answer 1

(i) $p\left(x\right)=x^2-3x+2=(x-1)(x-2)$

$p\left(1\right)=(1-1)\times (1-2)=0\times -1=0$

Also,

$p\left(2\right)=(2-1)(2-2)=-1\times 0=0$

Hence, 1 and 2 are the zeroes of the given polynomial.

(ii) $q\left(x\right)=x^2+x-6$

$q\left(2\right)=2^2+2-6=4-4=0$

Also,

$q(-3)=-3^2+-3-6=9-9=0$

Hence, 2 and -3 are the zeroes of the given polynomial.

(iii) $r\left(x\right)=x^2-3x$

$r\left(0\right)=0^2-3\times 0=0$

$r\left(3\right)=3^2-3\times 3=9-9=0$

Hence, 0 and 3 are the zeroes of the given polynomial.