Question

if alpha and beta are the zeroes of the polynomial x2+7x+7 find the value of 1/alpha +1/beta -2alphabeta

Answer 1

x²+7x+7=0
x= -b+ or - √b²-4ac/2a
x=-7 + or - √7²-4×7/2
x= -7 + or - √49-28/2
x= -7 + or - √21/2
so,
x= -7 + √21/2 (alpha)
and
x= -7 - √21/2 (beta)

note:- divided by 2 is for whole and not only for √21

Answer 2

∵α & β are roots of the given polynomial.
∴We get,
  α+β= -b/a = -7.
  αβ = c/a = 7.

 1/α + 1/β - 2αβ
= (α+β) /αβ - 2αβ
= -7/7 -2*7
= -15.(Ans)