Question

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

1, 1

Answer 1

1, 1

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

Given α + ß = `–b/a = 1`

αß = `c/a = 1`

If a = 1, b = -1, and c = 1

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