Question

1. Determine as raízes das seguintes equações incompletas do 2º grau:
a) 4x2 - 12x = 0
b) 5x2 - 45 = 0
c) 21x2 = 0
d) 9x2 - 27x = 0
e) 7x2- 343 = 0​

Answer 1

Resposta:

a) 4x² - 12x = 0

a = 4       b = -12       c = 0

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(-12) +- \sqrt{(-12)^{2} - 4 * 4 * 0} }{2*4}\\\\x = \frac{12+-\sqrt{144+0} }{8}\\\\x = \frac{12+-\sqrt{144} }{8}\\\\x = \frac{12+-12}{8}\\\\x' = \frac{12+12}{8}= \frac{24}{8}=3\\\\x' = \frac{12-12}{8}= \frac{0}{8}=0$

b) 5x² - 45 = 0

a = 5       b = 0       c = -45

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(0) +- \sqrt{(0)^{2} - 4 * 5 * -45} }{2*5}\\\\x = \frac{0+-\sqrt{0+900} }{10}\\\\x = \frac{0+-\sqrt{900} }{10}\\\\x = \frac{0+-30}{10}\\\\x' = \frac{0+30}{10}= \frac{30}{10}=3\\\\x' = \frac{0-30}{10}= \frac{-30}{10}=-3$

c) 21x² = 0

a = 21       b = 0       c = 0

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(0) +- \sqrt{(0)^{2} - 4 * 21 * 0} }{2*21}\\\\x = \frac{0+-\sqrt{0+0} }{42}\\\\x = \frac{0+-\sqrt{0} }{42}\\\\x = \frac{0+-0}{42}\\\\x' = \frac{0+0}{42}= \frac{0}{42}=0\\\\x' = \frac{0-0}{42}= \frac{0}{42}=0$

d) 9x² - 27x = 0

a = 9       b = -27       c = 0

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(-27) +- \sqrt{(-27)^{2} - 4 * 9 * 0} }{2*9}\\\\x = \frac{27+-\sqrt{729+0} }{18}\\\\x = \frac{27+-\sqrt{729} }{18}\\\\x = \frac{27+-27}{18}\\\\x' = \frac{27+27}{18}= \frac{54}{18}=3\\\\x' = \frac{27-27}{18}= \frac{0}{18}=0$

e) 7x²- 343 = 0​

a = 7       b = 0       c = -343

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(0) +- \sqrt{(0)^{2} - 4 * 7 * -343} }{2*7}\\\\x = \frac{0+-\sqrt{0+9604} }{14}\\\\x = \frac{0+-\sqrt{9604} }{14}\\\\x = \frac{0+-98}{14}\\\\x' = \frac{0+98}{14}= \frac{98}{14}=7\\\\x' = \frac{0-98}{14}= \frac{-98}{14}=-7$