Question

If alpha and beta arethe zeroes of polynomial 5x^+4x-9 then find alpha-beta

Answer 1

Since αα & ββ are roots of quadratic equation: 3x2+5x+7=03x2+5x+7=0 then we know that

α+β=−BA=−−53=53α+β=−BA=−−53=53

αβ=CA=−73αβ=CA=−73

1α3+1β3=α3+β3α3β3=(α+β)(α2+β2−αβ)(αβ)31α3+1β3=α3+β3α3β3=(α+β)(α2+β2−αβ)(αβ)3

=(α+β)((α+β)2−3αβ)(αβ)3=(α+β)((α+β)2−3αβ)(αβ)3

=(−5/3)((−5/3)2−3⋅7/3)(7/3)3=(−5/3)((−5/3)2−3⋅7/3)(7/3)3

=190343

Answer 2

5x^2+4x-9=0
x^2+(4x/5)-9/5=0.........dividing throughout by 5.
x^2+(4x/5)+a-a-9/5=0
a=(coefficient of x/2)^2
x^2+(4x/5)+(4/25)-(4/25)-(9/5)=0
(x+2/5)^2-49/25=0
(x+2/5)^2=49/25
x+2/5= + or -(7/5)......taking square roots on both sides.
x= + or -(7/5)-(2/5)
x=(+7-2)/5 or x=(-7-2)/5
=1 =-9/5
alpha is 1 and beta is -9/5