Question

The quadratic polynomials, the sum and product of whose zeroes are 7 and 12 are given by ______.

Answer 1

The quadratic polynomials, the sum and product of whose zeroes are 7 and 12 are given by k(x² – 7x + 12), where k is any constant.

Explanation:

If the zeros are α, β then for ax² + bx + c we have `α + β = -b/a` and `αβ = c/a`. Taking a = 1 gives –b = 7 ⇒ b = –7 and c = 12, so x² – 7x + 12 = 0.

Factoring: x² – 7x + 12 = (x – 3)(x − 4), so the zeros are 3 and 4 (sum 7, product 12).