Question

Find value of (a) for which (x-a)
is a factor of polynomial x^6-ax^5+x^4-ax^3+3x-a+2

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Answer 1

$x - a \: is \: a \: factor \: of \: \\ f(x) = {x}^{6} - {ax}^{5} + {x}^{4} - {ax}^{3} + 3x - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: a + 2 \\ \\ then \\ x - a = 0 \\ x = a \\ \\ on \: putting \: x = a \\ the \: equation \: will \: be \: satisfied \: to \: the \\ \: value \: of \: 0 \\ \\ substituting \: x = a \: in \: f(x) \\ \\ f(a) = {a}^{6} - a( {a}^{5} ) + {a}^{4} - a( {a}^{3} ) + \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3(a) - a + 2 \\ 0 = {a}^{6} - {a}^{6} + {a}^{4} - {a}^{4} + 3a - a + 2 \\ 0 = 2a + 2 \\ 2a = - 2 \\ a = \frac{ - 2}{2} \\ a = - 1$

Hence, a = -1.