If α and β are zeroes of the quadratic polynomial

Given that: α and β are the zeroes of the quadratic polynomial x2 − 6x + a and 3α + 2β = 20, then we have to find the value of a.

We have the following procedure.

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

$=6$...............(1)

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

$=a$.........(2)

$3 \alpha+2 \beta=20$

$\Rightarrow 2(\alpha+\beta)+\alpha=20$

$\Rightarrow \quad 2 \times 6+\alpha=20$

$\Rightarrow \quad \alpha=8$

Now, we are putting the value α in equation (1), we get

$8+\beta=6$

$\Rightarrow \quad \beta=-2$

From equation (2), we have

$a=8 \times(-2)$

$=-16$

Hence the value of a is −16.