Question

If a, ß are the roots of the equation x2 + px + p + q = 0, then find the value of a^2 + aB+B^2+q.​

Answer 1

Answer:

α,β be the roots of the equation x2+px+p2+q=0…(1).

We know that..

An equation formed by the two roots α,β is..

x2−(α+β)x+αβ=0…(2)

Now compairing (1) & (2) ,we get…

α+β=−p

& αβ=p2+q

The term α2+αβ+β2+q…(3) can be written as…

(α2+β2)+αβ+q

=(α+β)2–2αβ+αβ+q

=(α+β)2−αβ+q

=(−p)2−(p2+q)+q

=p2−p2−q+q

=0

Hence the required value of α2+αβ+β2+q is 0

Problem is done.