Question

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

Answer 1

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

$121 > 0 ; Rightarrow$ 2 корня.

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

Ответ: $x_1=2;;;;x_2=-0,2$

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

$105 > 0 ; Rightarrow$ 2 корня.

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

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