Question

Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:

(iv) $g\left(x\right)=x^3-6x^2+11x-6,$
$x=1,2,3$

Answer 1

Given:$g\left(x\right)=x^3-6x^2+11x-6;x=1,2,3$

We know that, if $f\left(a\right)=0;$ then $a$ is the zero of the polynomial $f\left(x\right)$

$\therefore f\left(1\right)=(1{)}^3-6\times (1{)}^2+11\times \left(1\right)-6$

$=1-6+11-6=0$

$f\left(2\right)=(2{)}^3-6\times (2{)}^2+11\times \left(2\right)-6$

$=8-24+22-6=0$

And $f\left(3\right)=(3{)}^3-6\times (3{)}^2+11\times \left(3\right)-6$

$=27-54+33-6=0$

$\because f\left(1\right)=0,f\left(2\right)=0andf\left(3\right)=0$

Hence, $x=1,2,3$ is the zero of $f\left(x\right)=x^3-6x^2+11x-6,$ verified.