If α, β are the zeros of a polynomial such that

Question:

If $\alpha, \beta$ are the zeros of a polynomial such that $\alpha+\beta=6$ and $\alpha \beta=4$ the write the polynomial.

Solution:

If the zeroes of the quadratic polynomial are α and β then the quadratic polynomial can be found as

$x^{2}-(\alpha+\beta) x+\alpha \beta$     ..........(1)

Substituting the values in (1), we get

$x^{2}-6 x+4$