Question

Resolva a equação do 2° grau a seguir:
a)x²+5x+6=0
b)3x²-2x-1=0​

Answer 1

$ax^2+bx+c, \,a\neq0 \to x=\dfrac{-b\pm\sqrt{\Delta}}{2a}, \Delta =b^2-4ac$

a) $a=1, b=5,c=6$

$\Delta = 5^2-4 \cdot 1 \cdot 6=25-24=1\\\\x=\dfrac{-5 \pm \sqrt{1}}{2\cdot1}=\dfrac{-5\pm1}{2} \\\\x_1 = \dfrac{-5+1}{2}= \dfrac{-4}{2}=-2\\x_2 = \dfrac{-5-1}{2}= \dfrac{-6}{2}=-3$

b) $a=3,b=-2,c=-1$

$\Delta = (-2)^2-4 \cdot 3 \cdot (-1)=4+12=16\\x=\dfrac{-(-2) \pm \sqrt{16}}{2\cdot3}=\dfrac{2\pm4}{6}\\\\x_1 = \dfrac{2+4}{6}= \dfrac{6}{6}=1\\\\x_2 = \dfrac{2-4}{6}= \dfrac{-2}{6}=-\dfrac{1}{3}$