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If alpha and bita are the …

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If alpha and bita are the zeros of the quadratic polynomial f(x) =ax square + bx +c, find the value of alpha square + bita square.

Posted by Diksha Bajaj 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 7 months ago

Let the two zeroes of the polynomials are α and β

where, {tex}\alpha = \frac {{ -b + \sqrt {b^2 - 4ac}}}{2a}{/tex} and {tex}\beta = \frac {{ -b - \sqrt {b^2 - 4ac}}}{2a}{/tex}

Now, {tex}\alpha + \beta {/tex}
{tex} = \frac{{ - b + \sqrt {{b^2} - 4ac} }}{{2a}}+ \left( {\frac{{ - b - \sqrt {{b^2} - 4ac} }}{{2a}}} \right){/tex}
{tex}= \frac{{ - b + \sqrt {{b^2} - 4ac} - b + \sqrt {{b^2} - 4ac} }}{{2a}}{/tex}
{tex}= \frac{{-2b }}{{2a}} = \frac{-b}{a}{/tex}

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