If α, β are the zeros of a polynomial such that α + β = −6 and αβ = −4,
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 $x^{2}+6 x-4$

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