Question

Find a quadratic polynomial, the sum and the product of whose zeroes are 4, 1.​

Answer 1

Let zeros be (α,β)

α+β=a−b=1

αβ=aC=−4

Polynominal is ax2+bx+C=0⇒x2+abx+aC=0

x2−x−4=0.

Answer 2

Let zeros be (α,β)

α+β=a−b=1

αβ=aC=−4

Polynominal is ax2+bx+C=0⇒x2+abx+aC=0

x2−x−4=0.