Question

Calcule a soma e os produtos das raizes da equação :
A : (x)^2 - 7 + 10 = 0
B: (2x)^2 - 10x -12 = 0
C: (8x)^2 - 7 = 0
D: 1 + 12x = (9x)^2

Answer 1

$a) \\ \\ x^2 - 7 + 10 = 0 \\ \\ x^2 + 3 = 0$

a = 1, b = 0, c = 3

$S = \dfrac{-b}{a} \\ \\ \\ S = \dfrac{-0}{1} \\ \\ S = 0 \\ \\ \\ P = \dfrac{c}{a} \\ \\ \\ P = \dfrac{3}{1} \\ \\ \\ P = 3$

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$b) \\ \\ \\ 2x^2 - 10x - 12 = 0$

a= 2, b = -10, c = -12

$S = \dfrac{-b}{a} \\ \\ \\ S = \dfrac{-(-10)}{2} \\ \\ \\S = \dfrac{10}{2} \\ S = 5 \\ \\ \\ P = \dfrac{c}{a} \\ \\ \\ P = \dfrac{-12}{2} \\ \\ \\ P = -6$

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c)

$8x^2 - 7 = 0$

a = 8, b = 0, c = -7

$S = \dfrac{-b}{a} \\ \\ \\ S = \dfrac{0}{8} \\ \\ \\S = 0 \\ \\ \\ P = \dfrac{-7}{8} \\ \\ \\ P = -\dfrac{7}{8}$

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d)

$1 + 12x = 9x^2 \\ \\ -9x^2 + 12 + 1 = 0$

a = -9, b = 12, c = 1

$S = \dfrac{-b}{a} \\ \\ \\ S = \dfrac{-12)}{-9} \\ \\ \\S = \dfrac{4}{3} \\ \\ \\ P = \dfrac{1}{-9} \\ \\ \\ P = -\dfrac{1}{9}$