Question

Determine as raizes das equacoes completas do 2° grau
A) 2x^2+x-1=0
B) 2x^2+2x-24=0
C) 3x^2-4x-2=-3
D) x^2+5x-2=-8

Answer 1

a) 2x² + x - 1 = 0 <<<<<<<<<<<<Delta = b² - 4acDelta = 1 - 4(2)(-1)Delta = 1 + 8Delta = 9
X = (-b +- raiz delta) / 2aX = (-1 +- 3) / 4x' = 2/4 = 1/2x" = -4/4 = -1

b) 2x² + 2x - 24 = 0 (:2)x² + x - 12 = 0 <<<<<<<<<<<<<<<<Delta = b² - 4acDelta = 1 - 4(1)(-12)Delta = 1 + 48Delta = 49
X = (-b +- raiz delta) / 2aX = (-1 +- 7) / 2x' = 6/2 = 3x" = -8/2 = -4
c) 3x² - 4x - 2 = -33x² - 4x + 1 = 0 <<<<<<<<<<<<<<<<Delta = b² - 4acDelta = 16 - 4(3)(1)Delta = 16 - 12Delta = 4
X = (-b +- raiz delta) / 2aX = (4 +- 2) / 6x' = 6/6 = 1x" = 2/6 = 1/3
d) 1/4x² + 5x/4 - 6 = 0mmc = 4x² + 5x - 24 = 0 <<<<<<<<<<<<<<<<Delta = b² - 4acDelta = 25 - 4(1)(-24)Delta = 25 + 96Delta = 121
X = (-b +- raiz delta) / 2aX = (-5 +- 11) / 2x' = 6/2 = 3x" = -16/2 = -8
e) x² + 5x - 2 = -8x² + 5x + 6 = 0 <<<<<<<<<<<<<<<<<<<<<Delta = b² - 4acDelta = 25 - 4(1)(6)Delta = 25 - 24Delta = 1
X = (-b +- raiz delta) / 2aX = (-5 +- 1) / 2x' = -4/2 = -2x" = -6/2 = -3