Question

Equações do 2 grau que possuem as raizes:
A) 1/2 e 1/3
B)-2/3 e 3
C)1/3 e -7

Answer 1

Boa noite Gabriel

a)
 
(x - 1/2)*(x - 1/3) = x² - x/2 - x/3 + 1/6 = 0
6x² - 3x - 2x + 1 = 0

6x² - 5x + 1 = 0 

b)

(x + 2/3)*(x - 3) = x² + 2x/3 - 9x/3 - 2 = 0

3x² - 7x - 6 = 0

c)

(x - 1/3)*(x + 7) = x² - x/3 + 21x/3 - 7/3 = 0

3x² + 20x - 7 = 0

Answer 2

vamos lá...

Vamos usar a formula 

x²-Sx+P=0   onde  S=x'+x"   e  P=x'.x"


$a) \\ x^2-( \frac{1}{2} + \frac{1}{3} )x+( \frac{1}{2} . \frac{1}{3} )=0 \\ \\ x^2-( \frac{3+2}{6} )x+ \frac{1}{6} =0 \\ \\ x^2- \frac{5}{6} x+ \frac{1}{6} =0 \\ \\ 6x^2-5x+1=0$ 

$b) \\ x^{2} -(- \frac{2}{3} +3)x+(- \frac{2}{3} .3)=0 \\ \\ x^{2} -( \frac{-2+9}{3} )x+(-2)=0 \\ \\ x^{2} - \frac{7}{3} x-2=0 \\ \\ 3x^2-7x-6=0$ 

$c) \\ x^2-( \frac{1}{3} -7)x+ \frac{1}{3} .(-7)=0 \\ \\ x^{2} -( \frac{1-21}{3} x- \frac{7}{3} =0 \\ \\ x^{2} -(- \frac{20}{3} )x- \frac{7}{3} =0 \\ \\ x^{2} + \frac{20}{3} x- \frac{7}{3} =0 \\ \\ 3x^2+20x-7=0$