Question

RESOLVA AS EQUAÇÕES USANDO A FORMULA DE BASKARA


A) 3x² - 7x + 4 = 0




B) 9y² - 12y + 4 = 0



C) 5x² + 3x + 5 = 0



D) 7x² + 14x = 0

Answer 1

Olá!

Questão a)

3x² - 7x + 4 = 0   →    a = 3  ,   b = -7   ,   c = 4

$\dfrac{-b\pm\sqrt{b^{2}-4\cdot a\cdot c} }{2\cdot a}~~~\to ~~~ \dfrac{-(-7)\pm\sqrt{(-7)^{2}-4\cdot 3\cdot 4} }{2\cdot 3}~~~=~~~\dfrac{7\pm\sqrt{1} }{6}\\ \\ \\ \\ \boxed{x'=\frac{4}{3}~~~e~~~x''=1 }$

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Questão b)

9y² - 12y + 4 = 0    →  a = 9  ,  b = -12   ,  c = 4

$\dfrac{-b\pm\sqrt{b^{2}-4\cdot a\cdot c} }{2\cdot a}~~~\to ~~~ \dfrac{-(-12)\pm\sqrt{(-12)^{2}-4\cdot 9\cdot 4} }{2\cdot 9}~~~=~~~\dfrac{12\pm\sqrt{0} }{18}\\ \\ \\ \\ \boxed{y=\frac{2}{3} }$

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Questão c)

5x² + 3x + 5 = 0   →  a = 5  ,  b = 3   ,  c = 5

$\dfrac{-b\pm\sqrt{b^{2}-4\cdot a\cdot c} }{2\cdot a}~~~\to ~~~ \dfrac{-3\pm\sqrt{3^{2}-4\cdot 5\cdot 5} }{2\cdot 5}~~~=~~~\dfrac{3\pm\sqrt{-81} }{10}~~~=~~~\dfrac{3\pm 9i}{10} \\ \\ \\ \\ \boxed{x'=\frac{3+9i}{10}~~~e~~~x''=\frac{3-9i}{10} }$

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Questão d)

7x² + 14x = 0    →  a = 7  ,  b = 14  ,  c = 0

$\dfrac{-b\pm\sqrt{b^{2}-4\cdot a\cdot c} }{2\cdot a}~~~\to ~~~ \dfrac{-14\pm\sqrt{14^{2}-4\cdot 7\cdot 0} }{2\cdot 7}~~~=~~~\dfrac{-14\pm\sqrt{196} }{14}~~~=~~~\dfrac{-14\pm 14}{14} \\ \\ \\ \\ \boxed{x'=0~~~e~~~x''=-2 }$

:)