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 = a2 + b2 + 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