Question

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

`-1/4 ,1/4`

Answer 1

Given: α + β = `-1/4`, αβ = `1/4`

Since ax² + bx + c = k[x² - (α + β)x + αβ]

Or `(ax^2 + bx + c)/k = x^2 - (-1/4x) + 1/4)`

Or `(ax^2 + bx + c)/k = (4x^2 + 4x + 1)/4`

Here k is a constant term, by comparing k = 4 

Hence, ax² + bx + c = `4x^2 + 4x + 1`

The quadratic polynomial is `4x^2 + 4x + 1`.