Question

If α and β are the zeros of the quadratic polynomial f(x) = 6x² + x − 2, find the value of $\frac{\mathrm{\alpha }}{\mathrm{\beta }}+\frac{\mathrm{\beta }}{\mathrm{\alpha }}$.

Answer 1

Since and are the zeros of the quadratics polynomial

f (x)=

sum of zeros =

Product of the zeros =

We have,

By substituting and we get ,

Hence, the value of is .