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

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

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

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

=

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

Other root of the given quadratic polynomial is β

f(x) = ax2 + bx + c

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

f(x) = ax2 + bx + c

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

f(x) = ax2 + bx + c

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

f(x) = ax2 + bx + c

Sum of the roots = =  =

Product of the roots = = =

=

+ = =

On substituting values, we get

=

= = b

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