Question

find alpha and beta are the zeros of the quadratic polynomial 3 X 2+ 5 x + 7 evaluate 1 upon Alpha 3 + 1 upon Beta 3

Answer 1

Since α & β are roots of quadratic equation: 3x^2+5x+7=0 then we know that

α+β=−B/A

       =−(−5/3)=5/3

αβ=C/A

    =−7/3

1/α^3+1/β^3=α^3+β^3/(αβ)^3
                  =(α+β)(α^2+β^2−αβ)/(αβ)^3

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

                  =190/343