Verify whether the following are True or False:
$0$ and $2$ are the zeroes of $t^{2}-2 t.$
A zero of a polynomial $p ( x )$ is a number $c$ such that $p ( c )=0$
Let $p(t)=t^{2}-2 t$
$\therefore \quad p(0)=(0)^{2}-2(0)=0$
And $\quad p(2)=(2)^{2}-2(2)=4-4=0$
Hence, $0$ and $2$ are zeroes of the polynomial $p(t)=t^{2}-2 t$.
If $\frac{x}{y}+\frac{y}{x}=-1(x, y \neq 0),$ the value of $x^{3}-y^{3}$ is
Factorise :
$3 x^{3}-x^{2}-3 x+1$
Verify whether $3$ and $5$ are zeros of the polynomial $x^{2}-x-6$ or not.
Evaluate the following products without multiplying directly
$88 \times 86$
Factorise
$\frac{x^{2}}{4}+\frac{3 x y}{5}+\frac{9 y^{2}}{25}$