Question

Find the value of k such that f(x)= x3-kx2+kx+2 has the factor x-2

Answer 1

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In the attachment..


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Answer 2

$solution \\ \\ x - 2 = 0 \\ x = 2 \\ putting \: value \: of \: x \: in \: equation \\ f(2) = 2 \times 3 - k \times 2 \times 2 + k \times 2 + 2 \\ f(2) = 6 - 4k + 2k + 2 \\ f(2) = 4 - 2k \\ \: \: \: \: 4 - 2k = 0 \ \: \\ \ \: \: 4 = 2k \\ \: \: 4 \div 2 = k \\ \: \: 2 = k \\ \: \: k = 2ans.$