Question

If alpha,bita are the roots of ax^2+bx+c=0,then the value of (1/(a×alpha)+b)+(1/(a×bita)+b)

Answer 1

If α,β are roots of ax2+bc+c=0

α+β=−ba

αβ=ca

OR

∴1aα+b+1aβ+b

=1aα+1aβ+2b

=α+βaαβ+2b

=−baaca+2b

=−b+2acac

1aα+b+1aβ+b

=1a(α+b/a)+1a(β+b/a)

=1aβ+1aα

=α+βaαβ

=−baaca=−bac

I hope you got your answer ✌️

Answer 2

Answer:

If α,β are roots of equation ax 2 +bx+c=0 then α+β= a−b &αβ= ac

i) (1+α)(1+β)

=1+α+β+αβ

=1+( a−b)+ ac =1+( ac−b)