Question:
If $\alpha, \beta$ are the zeros of a polynomial such that $\alpha+\beta=-6$ and $\alpha \beta=-4$, then write the polynomial.
Solution:
Let S and P denotes respectively the sum and product of the zeros of a polynomial
We are given $S=-6$ and $P=-4$. Then
The required polynomial $g(x)$ is given by
$g(x)=x^{2}-S x+P$
$g(x)=x^{2}-(-6) x+(-4)$
$=x^{2}+6 x-4$
Hence, the polynomial is $x^{2}+6 x-4$