Find the quadratic polynomial the sum and the product of whose zeroes are1/2,1,-3
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Hii friend,
(Alpha + Beta+ Gama) =1/2
(AlphaBeta + BetaGama+ GamaAlpha) = 1
And,
Alpha × Beta × Gama = -3
Therefore,
The required POLYNOMIAL = X³-(Alpha+Beta+Gama)X²+(AlpahBeta+BetaGama+GamaAlpha)X-Alpha × Beta × Gama
=> X³-(1/2)X²+(1)X-(-3) = 0
=> X³-X²/2 +X +3 = 0
=> 2X³-X²+2X+6 ÷ 2= 0
=> 2X³-X²+2X+6 = 0
Hence,
The polynomial = 2X³-X²+2X+6
HOPE IT WILL HELP YOU..... :-)
(Alpha + Beta+ Gama) =1/2
(AlphaBeta + BetaGama+ GamaAlpha) = 1
And,
Alpha × Beta × Gama = -3
Therefore,
The required POLYNOMIAL = X³-(Alpha+Beta+Gama)X²+(AlpahBeta+BetaGama+GamaAlpha)X-Alpha × Beta × Gama
=> X³-(1/2)X²+(1)X-(-3) = 0
=> X³-X²/2 +X +3 = 0
=> 2X³-X²+2X+6 ÷ 2= 0
=> 2X³-X²+2X+6 = 0
Hence,
The polynomial = 2X³-X²+2X+6
HOPE IT WILL HELP YOU..... :-)
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