Question

If α and β are the zeros of the quadratic polynomial f(x) = x² - 3x - 2, find a quadratic polynomial whose zeros are \(\frac{1}{2\alpha+\beta}\) and \(\frac{1}{2\beta+ \alpha}\)

Answer 1

f(x) = x² - 3x - 2

A quadratic equation when sum and product of its zeros is given by:

where k is a constant

Sum of the roots

Product of the roots

Sum of the zeros of new equation

Using (a + b)² = a² + b² + 2ab we get,

Product of the zeros of new equation