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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