Question

Find the zeroes of cubic polynomials
$x^2-x^3$
without drawing the graph of the polynomial.

Answer 1

$y=x^2-x^3$
Let
$f\left(x\right)=x^2-x^3$
$\Rightarrow x^2(1-x)$
$f\left(x\right)=0$
$\Rightarrow x^2=0$ and $1-x=0$

$\Rightarrow x=0$ and $x=1$
$\therefore$ Zeroes of the polynomial $f\left(x\right)$ are two.i.e.$0$ and $1$