Question:
If $a-b, a$ and $b$ are zeros of the polynomial $f(x)=2 x^{3}-6 x^{2}+5 x-7$, write the value of $a$.
Solution:
Let $a-b, a$ and $a+b$ be the zeros of the polynomial $f(x)=2 x^{3}-6 x^{2}+5 x-7$ then
Sum of the zeros $=\frac{-\text { Coefficient of } x^{2}}{\text { Coefficient of } x^{3}}$
$(a-d)+a+(a+d)=-\left(\frac{-6}{2}\right)$
$a+a+a-\mu+\mu=\frac{6}{2}$
$3 a=3$
$a=\frac{3}{3}$
$a=1$
Hence, the value of $a$ is 1 .