Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

4, 1

Answer 1

4,1

Let the quadratic polynomial be ax² + bx + c, and its zeroes be α and ß

Given α + ß = 4 = `–b/a`

αß = 1 = `c/a`

If a = 1, then b = -4, c = 1

Therefore, the quadratic polynomial is x² – 4x +1.