Question

Найдите произведение корней уравнения​

Answer 1

$3x^2 - 8x - 27 = 0$

$a = 3 \:\:\:\ b = -8 \:\:\:\ c = -27$

$D = b^2 - 4ac = (-8)^2 + 4 * 3 * 27 = 64 + 12 * 27 = 64 + 324 = 388$

$\sqrt{D} = \sqrt{388}$

$x_1 = \frac{8 + \sqrt{388}}{6}$

$x_2 = \frac{8 - \sqrt{388}}{6}$

$x_1 * x_2 = \frac{8 + \sqrt{388}}{6} * \frac{8 - \sqrt{388}}{6} = \frac{(8+\sqrt{388})(8-\sqrt{388})}{6*6} = \frac{64 - 8\sqrt{388} + 8\sqrt{388} -388}{36} = \frac{-324}{36} = -9$

$x_1 * x_2 = -9$