If alpha and beta are the …
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Sia ? 4 years, 10 months ago
It is given that {tex}\alpha{/tex} and {tex}\beta{/tex} are the zeros of the quadratic polynomial{tex}f(x)=ax^2+bx+c{/tex}
{tex}\therefore \quad \alpha + \beta = - \frac { b } { a } \text { and } \alpha \beta = \frac { c } { a }{/tex}
Now,
{tex}\alpha ^ { 2 } + \beta ^ { 2 } {/tex}
{tex}=\alpha ^ { 2 } + \beta ^ { 2 }+2\alpha\beta-2\alpha\beta{/tex}
{tex}= ( \alpha + \beta ) ^ { 2 } - 2 \alpha \beta{/tex}
{tex}\therefore \quad \alpha ^ { 2 } + \beta ^ { 2 } = \left( \frac { - b } { a } \right) ^ { 2 } - \frac { 2 c } { a } = \frac { b ^ { 2 } - 2 a c } { a ^ { 2 } }{/tex}
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