Question

resolva as seguintes equações:
a) x² - 6x + 7 = 0
b) x² + 3x - 28 = 0
c) x² + 8x + 16 = 0
d) 3x² - 2x + 1 = 0

Answer 1

Resposta:

a) ${3-\sqrt{2} ;3+\sqrt{2} }$

b) ${-7 ;4}$

c) -4

d) Não existe raiz real

Explicação passo-a-passo:

Vou resolver todas pela fórmula de Bhaskara, onde

$x1 = \frac{-b+\sqrt{b^{2}-4ac } }{2a} \\\\x2 = \frac{-b-\sqrt{b^{2}-4ac } }{2a}$

a)

$b^{2} -4*a*c\\(-6)^{2}-4*1*7\\36-28\\ 8\\\\\sqrt{8} =2\sqrt{2}$

$x1 = \frac{6+2\sqrt{2 } }{2} \\\\x2 = \frac{6-2\sqrt{2} }{2}\\\\x1 = 3-\sqrt{2} \\\\x2 = 3+\sqrt{2}$

b)

$b^{2} -4*a*c\\3^{2}-4*1*(-28)\\9+112\\ 121\\\\\sqrt{121} =11$

$x1 = \frac{-3+11 }{2} \\\\x2 = \frac{-3-11 }{2}\\\\x1 = 4 \\\\x2 = -7$

c)

$b^{2} -4*a*c\\8^{2}-4*1*16\\64-64\\ 0$

$x1 = \frac{-8+0 }{2} \\\\x2 = \frac{-8-0 }{2}\\\\x1 = -4 \\\\x2 = -4$

d)

$b^{2} -4*a*c\\(-2)^{2}-4*3*1\\4-12\\ -8\\\\\sqrt{-8}$

Δ DELTA negativo, não existe raiz real.