Question

Me ajudem, por favor!​

Answer 1

Olá!

Questão a)

3r² + 12r = 0

a = 3

b = 12

c = 0

$\dfrac{-b\±\sqrt{b^{2}-4.a.c} }{2.a}~~=~~\dfrac{-12\±\sqrt{12^{2}-4.3.0} }{2.3}~~=~~\dfrac{-12\±\sqrt{144} }{6}~~=~~\dfrac{-12\±12 }{6}\\ \\ \\ \\\boxed{r'=0}~~~~~~e~~~~~~\boxed{r''=-4}$

Resposta:

S = {0, -4}

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Questão b)

3s² - 300 = 0

a = 3

b = 0

c = -300

$\dfrac{-b\±\sqrt{b^{2}-4.a.c} }{2.a}~~=~~\dfrac{-0\±\sqrt{0^{2}-4.3.(-300)} }{2.3}~~=~~\dfrac{\±\sqrt{3600} }{6}~~=~~\dfrac{\±60 }{6}\\ \\ \\ \\\boxed{s'=10}~~~~~~e~~~~~~\boxed{s''=-10}$

Resposta:

S = {10, -10}

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Questão c)

x² - 5x + 6 = 0

a = 1

b = -5

c = 6

$\dfrac{-b\±\sqrt{b^{2}-4.a.c} }{2.a}~~=~~\dfrac{-(-5)\±\sqrt{(-5)^{2}-4.1.6} }{2.1}~~=~~\dfrac{5\±\sqrt{1} }{2}~~=~~\dfrac{5\±1 }{2}\\ \\ \\ \\\boxed{x'=3}~~~~~~e~~~~~~\boxed{x''=2}$

Resposta:

S = {3, 2}

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Questão d)

2x² + 4x - 6 = 0

a = 2

b = 4

c = -6

$\dfrac{-b\±\sqrt{b^{2}-4.a.c} }{2.a}~~=~~\dfrac{-4\±\sqrt{4^{2}-4.2.(-6)} }{2.2}~~=~~\dfrac{-4\±\sqrt{64} }{4}~~=~~\dfrac{-4\±8 }{4}\\ \\ \\ \\\boxed{x'=1}~~~~~~e~~~~~~\boxed{x''=-3}$

Resposta:

S = {1, -3}

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Questão e)

3x² - 9x - 30 = 0

a = 3

b = -9

c = -30

$\dfrac{-b\±\sqrt{b^{2}-4.a.c} }{2.a}~~=~~\dfrac{-(-9)\±\sqrt{(-9)^{2}-4.3.(-30)} }{2.3}~~=~~\dfrac{9\±\sqrt{441} }{6}~~=~~\dfrac{9\±21 }{6}\\ \\ \\ \\\boxed{x'=5}~~~~~~e~~~~~~\boxed{x''=-2}$

Resposta:

S = {5, -2}

:)