Question

resolva as equações do 2 grau em R

x^2-8x+15=0
x^2+10x+25=0
ax^2+4x+1=0
-x^2+12x-20=0

Answer 1

a) x² - 8x + 15 = 0

∆ = (-8)² - 4.1.15

∆ = 64 - 60

∆ = 4

$x = \frac{ - ( - 8) + - \sqrt{4} }{2 \times 1}$

$x = \frac{8 + - 2}{2}$

$x_{1} = \frac{8 - 2}{2} \\ x_{2} = \frac{8 + 2}{2}$

$x_{1} = 5 \\ x_{2} = 3$

b) x² + 10x + 25 = 0

∆ = 10² - 4.1.25

∆ = 100 - 100

∆ = 0

$x = \frac{ - 10 + - \sqrt{0} }{2 \times 1}$

$x = \frac{ - 10 + - 0}{2}$

$x = \frac{ - 10}{2}$

$x = - 5$

c) x² + 4x + 1 = 0

∆ = 4² - 4.1.1

∆ = 16 - 4

∆ = 12

$x = \frac{ - 4 + - \sqrt{12} }{2 \times 1}$

$x = \frac{ - 4 + - 2 \sqrt{3} }{2}$

$x_{1} = \frac{ - 4 - 2 \sqrt{3} }{2} \\ x_{2} = \frac{ - 4 + 2 \sqrt{3} }{2}$

$x_{1} = - 2 - \sqrt{3} \\ x_{2} = - 2 + \sqrt{3}$

d) -x² + 12x - 20 = 0

x² - 12x + 20 = 0

∆ = (-12)² - 4.1.20

∆ = 144 - 80

∆ = 64

$x = \frac{ - ( - 12) + - \sqrt{64} }{2 \times 1}$

$x = \frac{12 + - 8}{2}$

$x_{1} = \frac{12 -8 }{2} \\ x_{2} = \frac{12 + 8}{2}$

$x_{1} = 2 \\ x_{2} = 10$