Find cubic polynomial with zero values 7,1,2
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alpha = 7
beta = 1
gama = 2
alpha + beta + gama = 7+1+2 = 10
alpha × beta = 7 × 1 = 7
beta × gama = 1×2 = 2
gama × alpha = 2×7 = 14
alpha × beta × gama = 7×1×2 = 14
Therefore,
Required polynomial = X³-(alpha+ beta + gama)X²+(alpha beta+( beta gama+gama alpha)X + alpha beta gama.
= X³-(9)X²+(7+2+14)X- 14
= X³- 9X² + 23X-14 is required polynomial
beta = 1
gama = 2
alpha + beta + gama = 7+1+2 = 10
alpha × beta = 7 × 1 = 7
beta × gama = 1×2 = 2
gama × alpha = 2×7 = 14
alpha × beta × gama = 7×1×2 = 14
Therefore,
Required polynomial = X³-(alpha+ beta + gama)X²+(alpha beta+( beta gama+gama alpha)X + alpha beta gama.
= X³-(9)X²+(7+2+14)X- 14
= X³- 9X² + 23X-14 is required polynomial
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