Question

If Alpha and beta are the roots of ax2+bx+c=0 then find the quadratic equation of √alpha/beta,√beta/alpha

Answer 1

Answer:

ax2+bx+c=0

sum of roots, α+β=a−b

product of roots ⇒αβ=ac

⇒ Since eqn has roots as α2+2 & β2+2

So sum ⇒α2+2+β2+2

=α2+β2+4

=(α+β)2−2αβ+4

=(a−b)2−2(ac)+4

=a2+b2−2ac+4a2

Product =(α2+2)(β2+2)

=α2β2+2(α2+β2)+4