Question

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

1, 1

Answer 1

Given: α + β = 1, αβ = 1

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

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

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

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

Hence, ax² + bx + c = x² - x + 1

The quadratic polynomial is x² – x + 1.