Question

Determine the values of a and b, such that (x²-2x-3) is a factor of the polynomial x³-3x²-ax-b.

Answer 1

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Answer 2

$first \: solve \: eq. \\ {x}^{2} - 2x - 3 = 0\\ {x}^{2} - 3x + 1x - 3 = 0 \\ x(x - 3) + 1(x - 3) = 0\\ (x - 3)(x + 1) = 0 \\ x - 3 = 0 \: or \: x + 1 = 0 \\ x = 3 \: or \: - 1 \\ now \: put \: this \: value \: in \: the \: given \: polynmial \\ {3}^{3} - 3( {3)}^{2} + 3a - b = 0 \\ 27 - 27 + 3a - b = 0 \\ 3a - b = 0........(1) \\ {( - 1)}^{3} - 3( { - 1)}^{2} + ( - 1)a - b = 0 \\ - 1 - 3 - a - b = 0 \\ - 4 = a + b.......(2) \\ after \: solving \: we \: get \\ a = 1 \: and \: b = - 5$
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