Question

Розвяжіть рівняння x2+5x+6=0​

Answer 1

По теореме Виета:

x1+x2= -5

x1x2 = 6

x1= -2 ; x2= -3

Answer 2

$x^{2} + 5x + 6 = 0 \\\\ D = 5^{2} - 4\cdot 1\cdot 6 = 25 - 24 = 1$

$1 > 0 \; \Rightarrow$ два корня.

$x_{1,\;2} = \dfrac{-b \underline+ \sqrt{D}}{2a} \\\\ x_{1} = \dfrac{-5 + \sqrt{1}}{2} = \dfrac{-4}{2} = -2 \\\\ x_{2} = \dfrac{-5 - \sqrt{1}}{2} = \dfrac{-6}{2} = -3$

По теореме Виета:

$x_{1} + x_{2} = -5 \\ x_{1}\cdot x_{2} = 6 \\\\ x_{1} = -2 \\ x_{2} = -3$