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f(x) = 4x² + 4x - 3
{tex}\Rightarrow \quad f \left( \frac { 1 } { 2 } \right) = 4 \left( \frac { 1 } { 4 } \right) + 4 \left( \frac { 1 } { 2 } \right) - 3{/tex}
= 1 + 2 - 3 = 0
and {tex}f \left( - \frac { 3 } { 2 } \right) = 4 \left( \frac { 9 } { 4 } \right) + 4 \left( - \frac { 3 } { 2 } \right) - 3{/tex}
= 9 - 6 - 3 = 0
{tex}\therefore \frac { 1 } { 2 } , - \frac { 3 } { 2 }{/tex}are zeroes of polynomial 4x² + 4x - 3.
Sum of zeroes = {tex}\frac { 1 } { 2 } - \frac { 3 } { 2 } = - 1 = \frac { - 4 } { 4 }{/tex}
{tex}= - \frac { \text { Coefficient of } x } { \text { Coefficient of } x ^ { 2 } }{/tex}
Product of zeroes = {tex}\left( \frac { 1 } { 2 } \right) \left( - \frac { 3 } { 2 } \right) = \frac { - 3 } { 4 }{/tex}
{tex}= \frac { \text { Constant term } } { \text { Coefficient of } x ^ { 2 } }{/tex}
Verified.

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