If α and β are the zeros of the quadratic polynomial , then evaluate:

(i) (ii)

(iii) (iv)

(v) (vi)

(vii) (viii)

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

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

Other root of the given quadratic polynomial is β

Sum of the roots = = =

Product of the roots = = =

⇒ On substituting values, we get

⇒ =

=

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

Other root of the given quadratic polynomial is β

Sum of the roots = = =

Product of the roots = = =

⇒ On substituting values, we get

⇒

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

Other root of the given quadratic polynomial is β

Sum of the roots = = =

Product of the roots = = =

⇒ On substituting values, we get

⇒=

(v) Let one root of the given quadratic polynomial is

Other root of the given quadratic polynomial is β

Sum of the roots = = =

Product of the roots = = =

⇒= [Using (a + b)^{2} = a^{2} + b^{2} + 2ab]

On substituting values, we get

⇒=

⇒=

⇒=

(vi) Let one root of the given quadratic polynomial is

Other root of the given quadratic polynomial is β

Sum of the roots = = =

Product of the roots = = =

= =

⇒ On substituting values, we get

=

⇒ =

(vii) Let one root of the given quadratic polynomial is

Other root of the given quadratic polynomial is β

Sum of the roots = = =

Product of the roots = = =

=

⇒ = =

⇒ =

(viii) Let one root of the given quadratic polynomial is

Other root of the given quadratic polynomial is β

Sum of the roots = = =

Product of the roots = = =

=

⇒ + = =

On substituting values, we get

=

= = b

20