If 1 and are two zeroes of the polynomial , find its third zero.

Let

Since 1 and are the zeroes of , it follows that each one of and

is a factor of

Consequently, is a factor of .

On dividing by ,

f(x)=0⇒x2+x–2(x–5)=0⇒(x–1)(x+2)(x–5)=0⇒x=1 or x=–2 or x=5
f(x)=0 \Rightarrow\left(x^{2}+x-2\right)(x-5)=0 \\
\Rightarrow(x-1)(x+2)(x-5)=0 \\
\Rightarrow x=1 \text { or } x=-2 \text { or } x=5

Hence, the third zero is 5 .