If (a − b), a and (a + b) are zeros of the polynomial
Question:

If $(a-b), a$ and $(a+b)$ are zeros of the polynomial $2 x^{3}-6 x^{2}+5 x-7$, write the value of $a$.

Solution:

By using the relationship between the zeroes of the cubic ploynomial.
We have

Sum of zeroes $=\frac{-\left(\text { coefficient of } x^{2}\right)}{\text { coefficent of } x^{3}}$

$\Rightarrow a-b+a+a+b=\frac{-(-6)}{2}$

$\Rightarrow 3 a=3$

$\Rightarrow a=1$