If a − b, a and b are zeros of the polynomial

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 .