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Associate each 2nd degree equation with its respective roots. A) x2+6x+8=0 B)x2-5x-6=0

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Answer to a math question Associate each 2nd degree equation with its respective roots. A) x2+6x+8=0 B)x2-5x-6=0

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Frederik
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53 Answers
Para associar as equações do 2º grau às suas respectivas raízes, podemos utilizar a fórmula quadrática. A fórmula quadrática é dada por:

x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}

Onde "a", "b" e "c" são os coeficientes da equação quadrática ax^2 + bx + c = 0.

A) Vamos começar com a equação x^2 + 6x + 8 = 0.

Comparando com a forma geral ax^2 + bx + c = 0, temos:
a = 1, b = 6 e c = 8.

Aplicando a fórmula quadrática, temos:

x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} = \frac{{-6 \pm \sqrt{{6^2 - 4 \cdot 1 \cdot 8}}}}{{2 \cdot 1}}

Resolvendo a expressão dentro da raiz, obtemos:

x = \frac{{-6 \pm \sqrt{{36 - 32}}}}{{2}} = \frac{{-6 \pm \sqrt{{4}}}}{{2}} = \frac{{-6 \pm 2}}{{2}} = -3 \pm 1

Portanto, as raízes da equação x^2 + 6x + 8 = 0 são x = -3 + 1 = -2 e x = -3 - 1 = -4.

Portanto, a resposta para a equação A é (-2, -4).

B) Agora vamos resolver a equação x^2 - 5x - 6 = 0.

Comparando com a forma geral ax^2 + bx + c = 0, temos:
a = 1, b = -5 e c = -6.

Aplicando a fórmula quadrática, temos:

x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} = \frac{{-(-5) \pm \sqrt{{(-5)^2 - 4 \cdot 1 \cdot (-6)}}}}{{2 \cdot 1}}

Resolvendo a expressão dentro da raiz, obtemos:

x = \frac{{5 \pm \sqrt{{25 + 24}}}}{{2}} = \frac{{5 \pm \sqrt{{49}}}}{{2}} = \frac{{5 \pm 7}}{{2}}

Portanto, as raízes da equação x^2 - 5x - 6 = 0 são x = \frac{{5 + 7}}{{2}} = 6 e x = \frac{{5 - 7}}{{2}} = -1.

Portanto, a resposta para a equação B é (6, -1).

Respostas:
A) (-2, -4)
B) (6, -1)

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