Question

1)Resolva as equações do 2º grau usando a fórmula de Bhaskara.
a)x² - 7x + 6 = 0
b)x² + 12x + 30 = 0
c)9x² + 2x + 1 = 0
2) A equação incompleta 4x² – 16 = 0 possui solução? Se sim, quais são as raízes reais que a resolvem?
3) Encontre as raízes reais que formam o conjunto solução da equação do segundo grau: 2x² – 7x = 0

Answer 1

1.

$\boxed{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}$

a)

$x^2-7x+6=0$

$a=1,\ b=-7,\ c=6$

$x=\dfrac{-(-7)\pm\sqrt{(-7)^2-4(1)(6)}}{2(1)}=\dfrac{7\pm5}{2}$

$\boxed{x=1}\ \text{ou}\ \boxed{x=6}$

b)

$x^2+12x+30=0$

$a=1,\ b=12,\ c=30$

$x=\dfrac{-12\pm\sqrt{12^2-4(1)(30)}}{2(1)}=\dfrac{-12\pm\sqrt{24}}{2}=-6\pm\sqrt{6}$

$\boxed{x=-6-\sqrt{6}}\ \text{ou}\ \boxed{x=-6+\sqrt{6}}$

c)

$9x^2+2x+1=0$

$a=9,\ b=2,\ c=1$

$x=\dfrac{-2\pm\sqrt{2^2-4(9)(1)}}{2(9)}=\dfrac{-2\pm\sqrt{-32}}{18}=\dfrac{-2\pm4\sqrt{2}i}{18}=-\dfrac{1}{9}\pm\dfrac{2\sqrt{2}}{9}i$

$\boxed{x=-\dfrac{1}{9}-\dfrac{2\sqrt{2}}{9}i}\ \text{ou}\ \boxed{x=-\dfrac{1}{9}+\dfrac{2\sqrt{2}}{9}i}$

2.

$4x^2-16=0\ \to\ x^2=\dfrac{16}{4}=4\ \to\ x=\pm2$

$\boxed{x=-2}\ \text{ou}\ \boxed{x=2}$

3.

$2x^2-7x=0\ \to\ x(2x-7)=0$

$\boxed{x=0}\ \text{ou}\ \boxed{x=\dfrac{7}{2}}$