Question

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

Answer 1

Since and are the zeros of the quadratic polynomials

Sum of the zeros =

Product if zeros =

We have,

By substituting and we get ,

By substituting in we get ,

Taking square root on both sides we get

.

Hence, the value of is.