Question

решите с помощью дискримината
5x^2-9x-2=0
3x^2+11x+2=0

Answer 1

$5x^{2} - 9x - 2 = 0 \\\\ D = b^2-4ac=-9^{2} - 4\cdot 5\cdot (-2) = 81 - (-40) = 81 + 40 = 121$

$121 > 0 \; \Rightarrow$ 2 корня.

$\sqrt{121}=11\\\\x_{1,2}=\dfrac{-b\underline+\sqrt{D}}{2a}\\\\x_1=\dfrac{9+11}{2\cdot5}= \dfrac{20}{10} = 2\\\\x_2=\dfrac{9-11}{2\cdot5}=\dfrac{-2}{10}=-\dfrac1{5}=-0,2$

Ответ: $x_1=2;\;\;\;x_2=-0,2$

$2x^{2} + 11x + 2 = 0 \\\\ D = b^2-4ac=11^{2} - 4\cdot 2\cdot 2 = 121 - 16 = 105$

$105 > 0 \; \Rightarrow$ 2 корня.

$x_{1,2}=\dfrac{-b\underline+\sqrt{D}}{2a}\\\\x_1=\dfrac{-11+\sqrt{105}}{2\cdot2}=\dfrac{-11+\sqrt{105}}{4}\\\\x_2=\dfrac{-11-\sqrt{105}}{2\cdot2}=\dfrac{-11-\sqrt{105}}{4}$

Ответ: $x_1=\dfrac{-11+\sqrt{105}}{4};\;\;\;x_2=\dfrac{-11-\sqrt{105}}{4}$