Question

If α and β are the zeros of the quadratic polynomial f(x) = ax² + bx + c, then evaluate:

(i) α - β

(ii) \(\frac{1}{\alpha}\) - \(\frac{1}{\beta}\)

(iii)  \(\frac{1}{\alpha}\) + \(\frac{1}{\beta}\) - 2αβ

(iv) α²β + αβ²

Answer 1

(i) Let one root of the given quadratic polynomial is α

Other root of the given quadratic polynomial is β

Sum of the roots

Product of the roots

On substituting values, we get

(ii) Let one root of the given quadratic polynomial is α

Other root of the given quadratic polynomial is β

f(x) = ax² + bx + c 

Sum of the roots

Product of the roots

On substituting values, we get

(iii) Let one root of the given quadratic polynomial is α

Other root of the given quadratic polynomial is β

f(x) = ax² + bx + c 

Sum of the roots

Product of the roots

On substituting values, we get

(iv) Let one root of the given quadratic polynomial is α

Other root of the given quadratic polynomial is β

f(x) = ax² + bx + c 

Sum of the roots

Product of the roots

On substituting values, we get