if alpha and beta are the zeroes of the quadratic polynomial f(x)=3x^2-5x-2 then evaluate alpha^3+beta^3
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Answered by
4
Let alpha and beta be m and n
m + n = 5/3
mn = 2/3
alpha^3 + beta^3
= m^3 + n^3
= (m+n)^3 - 3mn ( m+n )
= (5/3)^3 - 3×(2/3) (5/3)
= ( 125/27) - (10/3)
= ( 125 - 90 ) /27
= 35 / 27
m + n = 5/3
mn = 2/3
alpha^3 + beta^3
= m^3 + n^3
= (m+n)^3 - 3mn ( m+n )
= (5/3)^3 - 3×(2/3) (5/3)
= ( 125/27) - (10/3)
= ( 125 - 90 ) /27
= 35 / 27
Answered by
2
(5+root21/6)^3 + (5-root21/6)^3 is the req sol
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