How do you factor #2x^2 + 3x -12#?

1 Answer
Jun 29, 2016

Answer:

2(x - x1)(x - x2)

Explanation:

y = 2x^2 + 3x - 12
Factored form of y:
y = a(x - x1)(x - x2)
Find x1 and x2, the 2 real roots of y. Use the improved quadratic formula.
#D = d^2 = b^2 - 4ac = 9 + 96 = 105# --> #d = +- sqrt105#
#x = -b/(2a) +- d/(2a) = -3/4 +- sqrt105/4#
Therefor,
#y = 2(x + 3/4 + sqrt105/4)(x + 3/4 - sqrt105/4)#