Question

If α and β are the zeroes of Q.P f(x) = ax² + bx + c ,
then evaluate :

i) $\frac{1}{a \alpha + b} + \frac{ 1 }{a \beta + b}$

ii) $\frac{ \beta }{a \alpha + b } + \frac{ \alpha }{a \beta + b}$

Answer 1

you can similarly do the second part.

Hope it helps:)

Answer 2

α and β are the roots of ax²+ bx +c

sum of roots = - b/a
α+ β = - b/ a

aα + aβ = - b

aα + b = - aβ ------------(1).
aβ + b = - aα ------------(2)

use. this in (1)

1/- aβ + 1/- aα = -1/a( 1/α + 1/β)

= -1/a ( α + β)/αβ

=-1/a( -b/a)/(c/a)

= b/ca



again,
β/-aβ + α/-aα

= -1/a - 1/a

= - 2/a