Question

If $\alpha$ and $\beta$ are zeros of $x^2-6x+a$ and $3\alpha +2\beta =20$. find the value of $a$.

Answer 1

Given equation

$x^2-6x+a$

And the roots are $\alpha$ and $\beta$.

Now,

$3\alpha +2\beta =20......\left(1\right)$

We know that,

Sum of roots $=-\frac{coeff.ofx}{coeff.of{x}^2}$

$\alpha +\beta =-\frac{-6}{1}=6$

$\alpha +\beta =6......\left(2\right)$

From equation (1) and (2) to, and we get,

$\alpha =8$ and $\beta =-2$

Now,

Product of roots$=\frac{\text{constant}\text{term}}{\text{coeff}\text{.}\text{of}{\text{x}}^{\text{2}}}$

$\alpha .\beta =\frac{a}{1}$

$\Rightarrow 8\times (-2)=a$

$\Rightarrow a=-16$

Hence, this is the answer.