Question

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

Answer 1

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

where k is a constant

Consider the polynomial f(x) = x² - 1,

Sum of the roots

Product of the roots

New equation have zeroes as \(\frac{2\alpha}{\beta}\) and \(\frac{2\beta}{\alpha}\),

Sum of the zeros of new equation \(\frac{2\alpha}{\beta}\) and \(\frac{2\beta}{\alpha}\)

[Using (a + b)² = a² + b² + 2ab]

Product of the zeros of new equation