Question

resolva as equações do 2° grau, utilizando a fórmula de bhaskara​

Answer 1

Resposta:

- Formula ➳ X = -b ± √b² - 4 . a . c / 2 . a

a) x² - 6x + 8 = 0  ➛ a = 1      b = - 6      c = 8

» calculo «

X = -b ± √b² - 4 . a . c / 2 . a

X = -(-6) ± √(-6)² - 4 . 1 . 8 / 2 . 1

X = -(-6) ± √36 - 4 . 1 . 8 / 2 . 1

X = -(-6) ± √36 - 4 . 8 / 2 . 1

X = -(-6) ± √36 - 32 / 2 . 1

X = -(-6) ± √4 / 2 . 1

X = -(-6) ± 2 / 2 . 1

X = -(-6) ± 2 / 2

X = 6 ± 2 / 2   ➳ X' = 6 + 2 / 2 ➳ X' = 8 / 2 ➳ X' = 4

                      ➳ X" = 6 - 2 / 2 ➳ X" = 4 / 2 ➳ X" = 2

➳ S = {4 , 2}

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b) x² + 3x - 28 = 0 ➛ a = 1      b = 3      c = -28

» calculo «

X = -b ± √b² - 4 . a . c / 2 . a

X = -3 ± √3² - 4 . 1 . (-28) / 2 . 1

X = -3 ± √9 - 4 . 1 . (-28) / 2 . 1

X = -3 ± √9 - 4 . (-28) / 2 . 1

X = -3 ± √9 - (-112) / 2 . 1

X = -3 ± √9 + 112 / 2 . 1

X = -3 ± √121 / 2 . 1

X = -3 ± 11 / 2 . 1

X = -3 ± 11 / 2 ➳ X' = -3 + 11 / 2 ➳ X' = 8 / 2 ➳ X' = 4

                      ➳ X" = -3 - 11 / 2 ➳ X" = -14 / 2 ➳ X" = 7

➳ S = {4 , 7}

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c) 4x² - 12x = 0 ➛ a = 4      b = -12      c = 0

» calculo «

X = -b ± √b² - 4 . a . c / 2 . a

X = -(-12) ± √(-12)² - 4 . 4 . 0 / 2 . 4

X = -(-12) ± √144 - 4 . 4 . 0 / 2 . 4

X = -(-12) ± √144 - 16 . 0 / 2 . 4

X = -(-12) ± √144 - 0 / 2 . 4

X = -(-12) ± √144 / 2 . 4

X = -(-12) ± 12 / 2 . 4

X = -(-12) ± 12 / 8

X = 12 ± 12 / 8 ➳ X' = 12 + 12 / 8 ➳ X' = 24 / 8 ➳ X' = 3

                      ➳ X" = 12 - 12 / 8 ➳ X" = 0 / 8 ➳ X" = 0

➳ S = {3 , 0}

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d) x² + 8x + 16 = 0 ➛ a = 1      b = 8      c = 16

» calculo «

X = -b ± √b² - 4 . a . c / 2 . a

X = -8 ± √8² - 4 . 1 . 16 / 2 . 1

X = -8 ± √64 - 4 . 1 . 16 / 2 . 1

X = -8 ± √64 - 4 . 16 / 2 . 1

X = -8 ± √64 - 4 . 16 / 2 . 1

X = -8 ± √64 - 64 / 2 . 1

X = -8 ± √0 / 2 . 1

X = -8 ± 0 / 2 . 1

X = -8 ± 0 / 2 ➳ X' = -8 + 0 / 2 ➳ X' = -8 / 2 ➳ X' = -4

                      ➳ X" = -8 - 0 / 2 ➳ X" = -8 / 2 ➳ X" = -4

➳ S = {-4 , -4}

=================================================================

e) 3x² - 2x - 8 = 0 ➛ a = 3      b = -2      c = -8

» calculo «

X = -b ± √b² - 4 . a . c / 2 . a

X = -(-2) ± √(-2)² - 4 . 3 . (-8) / 2 . 3

X = -(-2) ± √4 - 4 . 3 . (-8) / 2 . 3

X = -(-2) ± √4 - 12 . (-8) / 2 . 3

X = -(-2) ± √4 - (-96) / 2 . 3

X = -(-2) ± √4 + 96 / 2 . 3

X = -(-2) ± √100/ 2 . 3

X = -(-2) ± 10/ 2 . 3

X = -(-2) ± 10/ 6

X =2 ± 10/ 6 ➳ X' = 2 + 10 / 6 ➳ X' = 12 / 6➳ X' = 2

                    ➳ X" = 2 - 10 / 6 ➳ X" = -8 / 6 ➳ X" =-4/3

➳ S = {2 , -4/3}

(ﾉ◕ヮ◕)ﾉ*:･ﾟ✧ Espero ter ajudado, Bons estudos ◕3◕