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 $=\frac{-\left(\text { coefficient of } x^{2}\right)}{\text { coefficent of } x^{3}}$
$\Rightarrow a-b+a+a+b=\frac{-(-6)}{2}$
$\Rightarrow 3 a=3$
$\Rightarrow a=1$
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