Question

разложить на множители квадратный трёхчлен -6х²-х+5; х²-5х-6.
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Answer 1

Ответ:

$-6x^{2} -x+5 = 0\\6x^{2} + x -5 = 0\\D = b^{2} - 4ac = 1^{2} - 4*6*(-5) = 1 + 120 = 121\\x_{1} = \frac{-b-\sqrt{D} } {2a} = \frac{-1 - 11}{2 * 6} = -1;\\x_{2} = \frac{-b+\sqrt{D} } {2a} = \frac{-1 + 11}{2 * 6} = \frac{5}{6} ;\\\\6(x+1)(x-\frac{5}{6} ) = 0;$

$x^{2} -5x-6 = 0\\D = b^{2} - 4ac = (-5)^{2} - 4 * 1 * (-6) = 49;\\x_{1} = \frac{-b - \sqrt{D} }{2a} = \frac{5 - 7}{2 * 1} = -1;\\x_{2} = \frac{-b - \sqrt{D} }{2a} = \frac{5 + 7}{2 * 1} = 6;\\\\(x+1)(x-6) = 0$