Question

without finding the value of roots alfa and bita of polynomial p(x)=x²-5x+6
Find the valve of 1/alfa+1/bita and
alfa³+bita³
​

Answer 1

1/alpha +1/ beta = (alpha)+ (beta) / (alpha)(beta)

-b/a / c/a = -b/c = 5/6

5/6 is the value of 1/(alpha) + 1/(beta)

and,

alpha³ + beta³ = (alpha+beta)³ - 3((alpha)(beta) (alpha+beta)

125 -3(6)(5) = 125-90 = 35

So 35 is the value of alpha³+beta³

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