The general form of quadratic polynomial having α,β as its zeroes is
= x2 – (sum of zeroes)x + product of zeroes.
= x2 – (α + β) x + αβ, here given (α + β) = -3 and
(α2 + β2 ) = 17
∴ (α + β)2 = α2 + β2 + 2αβ
(-3)2 = 17 + 2αβ => 2αβ = 9 – 17 = -8
∴ αβ = \(-\frac{8}{2}\) = -4
∴ The required polynomial is x2 – (-3) x + (-4) = x2 + 3x – 4 is required quadratic polynomial.