Question

Resolva as equações do 2º grau em R

a) x²-8x+15=0

b) x²+10x+25=0

c)3x²+4x+1=0

d) -x²+ 12x-20=0

Answer 1

Explicação passo-a-passo:

$a)x {}^{2} - 8x + 15 = 0$

$a = 1 \: \: b = - 8 \: \: \: c = 15$

$delta = b {}^{2} - 4ac$

$delta = ( - 8) {}^{2} - 4.1.15 = 64 - 60 = 4$

$\sqrt{4} = 2$

$x1 = \frac{ - ( - 8) + 2}{2.1} = \frac{8 + 2}{2} = \frac{10}{2} = 5$

$x2 = \frac{ - ( - 8) - 2}{2.1} = \frac{8 - 2}{2} = \frac{6}{2} = 3$

$b)x {}^{2} + 10x + 25 = 0$

$a = 1 \: \: \: b = 10 \: \: c = 25$

$delta = b {}^{2} - 4ac$

$delta = 10 {}^{2} - 4.1.25 = 100 - 100 = 0$

$\sqrt{0} = 0$

$x1 = x2 = \frac{ - 10 + 0}{2} = \frac{ - 10}{2} = - 5$

$c)3x {}^{2} + 4x + 1 = 0$

$a = 3 \: \: b = 4 \: \: \: c = 1$

$delta = b {}^{2} - 4ac$

$delta = 4 {}^{2} - 4.3.1 = 16 - 12 = 4$

$\sqrt{4} = 2$

$x1 = \frac{ - 4 + 2}{2.3} = \frac{ - 2}{6} = \frac{ - 1}{3}$

$x2 = \frac{ - 4 - 2}{2.3} = \frac{ - 6}{6} = - 1$

$d) - x {}^{2} + 12x - 20 = 0$

$a = - 1 \: \: b = 12 \: \: \: c = - 20$

$delta = b {}^{2} - 4ac$

$delta = 12 {}^{2} - 4. - 1. - 20 = 144 - 80 = 64$

$\sqrt{64} = 8$

$x1 = \frac{ - 12 + 8}{2. - 1} = \frac{ - 4}{ - 2} = 2$

$x2 = \frac{ - 12 - 8}{2. - 1} = \frac{ - 20}{ - 2} = 10$