Question

if 4/27=2^a.3^b, then find quadratic polynomial with zeroes a and b

Answer 1

Alpha and beta are the zeros of the quadratic polynomial 3x^2 +5x +7

Alph + beta = -5/3

Alpha *beta =7/3

Now

1/Alpha ^3 +1/beta ^3

=(Alpha ^3 +beta ^3)/(Alpha *beta)^3

={(Alpha +beta)^3–3Alpha*beta(Alpha +beta)}/(Alpha *beta)^3

={(-5/3)^3 -3(7/3)(-5/3)}/(7/3)^3

={(-125/27)+35/3}/(343/27)

={(-125+315)/27}/(343/27)

=(190/27)*(27/343)

=190/343

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