Question

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

`-1/4 ,1/4`

Answer 1

`-1/4 ,1/4`

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

Given α + ß = `-1/4 = –b/a`

αß = `1/4 = c/a`

If a = 4, b = 1, c = 1

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