How do you factor and solve #3x^3 + 4x^2 - 15x = 0#?

1 Answer
Nghi N.
Jun 29, 2016

#x = 0, x = 5/3, x = -3#

Explanation:

#f(x) = xy = x(3x^2 + 4x - 15) = 0#.
Factor y by using the new AC Method (Socratic Search)
Converted trinomial: #y' = x^2 + 4x - 45#.
Find p' and q' that have opposite signs (ac < 0), and that has their
sum (b = 4) and their product (c = -45).
They are; p' = -5 and q' = 9.Back to trinomial y, #p = (p')/a = -5/3 = -5/3#, and #q = (q')/a = 9/3 = 3#
Factored form of y:
#y = 3(x - 5/3)(x + 3) = (3x - 5)(x + 3).#
Finally, the real roots of f(x) = x(3x - 5)(x + 3) are:
#x = 0, x = 5/3, and x = -3#

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