Question

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

`1/4 , -1`

Answer 1

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

Given α + ß = `1/4 = –b/a`

αß = -1 = `c/a`

If a = 4, b = -1, c = -4

The quadratic polynomial is 4x² – x -4.