Question

If alpha,beta ,gamma are zeros of P(x)=6x³+3x²-5x+1, find the of alpha^-1+beta^-1+gamma^-1.

Answer 1

Hii friend,

P(X) = 6X³+3X²-5X+1

Sum of zeros = (Alpha + Beta + Gama) = -3/6 = -1/2.

Alpha × Beta + Beta × Gama + Gama × Alpha = -5/6

And,

Alpha × Beta × Gama = -1/6

Therefore,

Alpha^-1 + ẞ^-1 + Gama^-1

=> 1/ Alpha + 1/ß + 1/ Gama

=> Beta Gama + Gama Alpha + Alpha × Beta/Alpha × Beta × Gama

=> (-5/6/-1/6) = 5


HOPE IT WILL HELP YOU..... :-)

Answer 2

P(X) = 6X³+3X²-5X+1
Sum of zeros = (Alpha + Beta + Gama) = -3/6 = -1/2.
Alpha × Beta + Beta × Gama + Gama × Alpha = -5/6
And,
Alpha × Beta × Gama = -1/6
Therefore,
Alpha^-1 + ẞ^-1 + Gama^-1
=> 1/ Alpha + 1/ß + 1/ Gama
=> Beta Gama + Gama Alpha + Alpha × Beta/Alpha × Beta × Gama
=> (-5/6/-1/6) = 5

HOPE IT WILL HELP YOU..... :-)