Question

resolver as seguintes equações do segundo grau. ....
A) 7 x² - 7 x = 0
B)  x² - 7 x = 0
C) x² + 5 x = 0
D) 4 x² - 9 x= 0
E) 3  x² + 5x= 0
F) x² + x. (x-6) =0
G) x. ( x + 3) = 5x
alguém pode ajudar pfvr

Answer 1

$1)7x^2-7x=0\\\\7x(x-1)=0\\7x'=0\rightarrow x'=0\\x''-1=0\rightarrow x''=1\\\\x=\{0;1\}\\\\2)x^2-7x=0\\\\x(x-7)=0\\x'=0\\x''-7=0\rightarrow x''=7\\\\x'=\{0;7\}$
$2)x^2 + 5 x = 0\\\\x(x+5)=0\\x'=0\\x''+5=0\rightarrow x''=-5\\\\x=\{-5;0\}\\\\3)4 x^2 - 9 x= 0\\\\x(4x-9)=0\\x'=0\\4x''-9=0\rightarrow4x''=9\rightarrow x''=\frac{9}{4}\\\\x=\{0;\frac{9}{4}\}$
$5) 3 x^2 + 5x= 0\\\\x(3x+5)=0\\x'=0\\3x''+5=0\rightarrow3x''=-5\rightarrow x''=-\frac{5}{3}\\\\6)x^2 + x (x-6) =0\\\\x^2+x^2-6x=0\\2x^2-6x=0\\2x(x-3)=0\\2x'=0\rightarrow x'=0\\x''-3=0\rightarrow x''=3\\\\x=\{0;3\}$
$7) x ( x + 3) = 5x\\\\x^2+3x=5x\\x^2+3x-5x=0\\x^2-2x=0\\x(x-2)=0\\x'=0\\x''-2=0\rightarrow x''=2\\\\x=\{0;2\}$