Question

If alpha and beta are the zeroes of the polynomial ax2+bx +c,then find 1/alpha2+1/beta2.

Answer 1

Answer:

Given the polynomial: ax²+bx+c

Given, zeros: α and β

Using the relation between the zeros and coefficients, we have:

α+β= -b/a

αβ= c/a

Now

\frac{1}{ \alpha ^2} + \frac{1}{\beta^2} = \frac{ \beta ^2+ \alpha ^2}{ \alpha ^2 \beta ^2}

= \frac{( \alpha +\beta)^2-2 \alpha \beta }{( \alpha \beta )^2}

Substituting the values:

\frac{ (\frac{-b}{a})^2- \frac{2c}{a} }{ (\frac{c}{a})^2 } = \frac{ \frac{b^2}{a^2}- \frac{2c}{a} }{ \frac{c^2}{a^2} } = \frac{ \frac{b^2-2ac}{a^2}}{ \frac{c^2}{a^2} }= \frac{b^2-2ac}{a^2}* \frac{a^2}{c^2}= \frac{b^2-2ac}{c^2}

Hope its helps

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

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