Question

PELO AMOR DE DEU ALGUM ME AJUDA 1) Resolva as equações do 2o grau: a) x2 + 5x = 0 b) x2 - 36 = 0 c) 2x2 + 32 = 0 d) 2x2 + 32x = 0 e) 3x2 - 5x = 0 f) 3x2 - 75 = 0 g) 6x2 - 10x = 0 h) 5x2 + 15x = 0 i) 3x2 - 12 = 0 j) 7x2 + 21x = 0 k) 5x2 - 10 = 0 l) 4x2 - 36 = 0

Answer 1

Resposta:

a) x=0     e  x=-5

b) x = 6 e x= -6

c) x = ∄ (não existe raiz negativa)

d) x = 0 e x =-16

e)  x = 0 e x = 5/3

f)  x = 5 e x = -5

g) x = 0 e x = 5/3

h)  x = 0 e x = -3

i)  x = 2 e x = -2

j) x = 0 e x = -3

k)  x = √2 e x = -√2

l)  x = 3 e x = -3

Explicação passo-a-passo:

a)

$x^{2} +5x=0\\x(x+5)=0\\\\ x=0 \\ e\\x+5=0 > x=-5$

b)

$x^{2} - 36 = 0\\ x^{2} = 36\\x=\sqrt{36} \\x= ±6$

c)

$2x^{2} + 32 = 0\\2x^{2} = -32\\x^{2} =-\frac{32}{2}\\x^{2} = -16\\ x= \sqrt{-16}$

d)

$2x^{2} + 32x = 0\\2x(x+16) =0\\2x=0\\ x=0\\\\x+16 =0\\x=-16$

e)

$3x^{2} - 5x = 0\\x(3x -5)=0\\ x=0\\\\3x-5=0\\3x=5\\x=\frac{5}{3}$

f)

$3x^{2} - 75 = 0\\3x^{2} =75\\x^{2} = \frac{75}{3} \\x^{2} = 25\\x = \sqrt{25} \\x = +-5$

g)

$6x^{2} - 10x = 0\\2x(3x-5) = 0\\2x=0\\\\3x-5=0\\3x=5\\ x=5/3$

h)

$5x^{2} + 15x = 0\\5x(x+3)=0\\\\5x=0\\x=0\\\\x+3=0\\x=-3$

i)

$3x^{2} - 12 = 0\\3x^{2} =12 \\x^{2} = \frac{12}{3} \\x^{2} = 4\\x= \sqrt{4} \\x=+-2$

j)

$7x^{2} + 21x = 0\\7x(x+3)=0\\\\7x=0\\x=0\\\\x+3=0\\x=-3$

k)

$5x^{2} - 10 = 0\\5x^{2}=10\\x^{2} = \frac{10}{5}\\ x^{2} =2\\x=+-\sqrt{2}$

l)

$4x^{2} - 36 = 0\\ 4x^{2} =36\\x^{2} = \frac{36}{4}\\x^{2} =9\\x=\sqrt{9}\\x=+-3$