Question

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

Answer 1

Since α and β are the zeros of the quadratic polynomial

The roots are

Let S and P denote respectively the sum and product of zeros of the required polynomial. Then,

Taking least common factor we get,

Hence, the required polynomial is given by,

Hence, required equation is Where k is any non zero real number.