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.​

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.​

About the author
Amaya

1 thought on “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.​”

  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.

    Reply

Leave a Comment