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
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
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.