Question

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

`0, sqrt5`

Answer 1

Given: α + β = 0, αβ = `sqrt5`

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

Or `(ax^2 + bx + c)/k = (x^2 - 0x + sqrt5)`

or `(ax^2 + bx + c)/k = (x^2 + sqrt5)/1`

Here k is a constant term, by comparing k = 1

Hence, ax² + bx + c = `x^2 + sqrt5`

The quadratic polynomial is `x^2 + sqrt5`.