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Question
Verify whether the indicated numbers is zeros of the polynomials corresponding to them in the following case:
\[p(x) = x^3 - 6 x^2 + 11x - 6, x = 1, 2, 3\]
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Solution
To check whether the given number is the zero of the polynomial or not we have to find p(1),p(2),and p(3)
`p(x) = x^3 - 6x^2 + 11x - 6`
`p(1) = (1)^3 - 6 xx (1)^2 + 11 xx (1) - 6`
` = 1-6 xx 1 + 11 xx 1 - 6`
` = 12 - 12 = 0`
`p(2) = (2)^3 - 6 xx (2)^2 + 11 xx (2) - 6`
` = 8-6 xx 4 + 11 xx 2 -6`
` = 8-24 + 22 -6`
` = 30 - 30`
p(2) = 0
And
`p(3) = (3)^3 - 6 xx (3)^2 + 11 xx 3 - 6`
` = 27 - 6 xx 9 + 11 xx 3 -6`
` = 27 - 54 + 33 -6`
` = 60 - 60`
p(3) = 0
Hence, x = 1, 2, 3 are the zeros of the polynomial p(x).
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