Question

If alpha and beta are roots of equation ax^2+bx+c =0then find the value of ​

Answer 1

Answer:

-2/a

Step-by-step explanation:

α and β are roots of equation

ax²+bx+c =0

so α+β=-b/a

αβ=c/a

======================

hence

β/(aα+b) +α/(aβ+b)

=[ β(aβ+b)+α(aα+b) ] / (aα+b)(aβ+b)

= ( aβ²+bβ+aα²+bα) / (a²αβ+abα+abβ+b²)

=[ a(α²+β²) +b(α+β) ]/ [( a²αβ+ab(α+β) +b² ]

=[ a { (α+β)²-2αβ} +b(α+β) ] / [( a²αβ+ab(α+β) +b² ]

===============

putting values we get

={ a(  b²/a²-2c/a) +b*-b/a] /(a²*c/a+ab*-b/a+b²)

={ b²/a-2c-b²/a)/(ca-b²+b²)

=-2c/ca

=-2/a

Please comment if the answer is correct