Question

EXERCÍCIOS SOBRE EQUAÇÕES DE 2°GRAU, A PARTIR DA FÓRMULA DE BHÁSKARA
1) x² + x – 6 = 0
2) x² + 2x - 3 = 0
3) -x² -4x +5 = 0
4) x² + 2x – 24 = 0
5) x2 - 3x -4 = 0

Answer 1

Fórmula Quadrática de Brahmagupta:

$ax^2+bx+c=0\ \therefore\\\\ \therefore\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

1. $x^2+x-6=0$

$a=1;\ b=1;\ c=-6\\\\ x=\dfrac{-1\pm\sqrt{1^2-4(1)(-6)}}{2(1)}=\dfrac{-1\pm\sqrt{25}}{2}=\dfrac{-1\pm5}{2}\\\\ x_1=2;\ x_2=-3$

2. $x^2+2x-3=0$

$a=1;\ b=2;\ c=-3\\\\ x=\dfrac{-2\pm\sqrt{2^2-4(1)(-3)}}{2(1)}=\dfrac{-2\pm\sqrt{16}}{2}=-1\pm2\\\\ x_1=1;\ x_2=-3$

3. $-x^2-4x+5=0$

$a=-1;\ b=-4;\ c=5\\\\ x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(-1)(5)}}{2(-1)}=\dfrac{4\pm\sqrt{36}}{-2}=-2\mp3\\\\ x_1=-5;\ x_2=1$

4. $x^2+2x-24=0$

$a=1;\ b=2;\ c=-24\\\\ x=\dfrac{-2\pm\sqrt{2^2-4(1)(-24)}}{2(1)}=\dfrac{-2\pm\sqrt{100}}{2}=-1\pm5\\\\ x_1=4;\ x_2=-6$

5. $x^2-3x-4=0$

$a=1;\ b=-3;\ c=-4\\\\ x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(1)(-4)}}{2(1)}=\dfrac{3\pm\sqrt{25}}{2}=\dfrac{3\pm5}{2}\\\\ x_1=4;\ x_2=-1$