Question

if alpha and beta are the zeroes of polynomial ax2+ bx+ c then find the value of 1/alpha2+1/beta2

Answer 1

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

Answer 2

Answer:

Step-by-step explanation: