What is the solution set for #4x^2 - 5x < 6#?

1 Answer
Aug 7, 2015

Answer:

Solve #4x^2 - 5x < 6#

Ans: #(-3/4, 2)#

Explanation:

Bring the inequality to standard form:
#f(x) = 4x^2 - 5x - 6 < 0#
First, solve #f(x) = 4x^2 - 5x - 6 = 0# (1) to get the 2 real roots.
I use the new Transforming Method. (Google, Yahoo)
Transformed equation #f'(x) = x^2 - 5x + 24# (2). Roots have opposite signs.
Factor pairs of 24 -> ...(-2, 12)(-3, 8). This sum is 5 = -b. Then, the 2 real roots of (2) are: -3 and 8.
Back to original equation (1), the 2 real roots are: #-3/4# and #8/4 = 2.#
Find the solution set of the inequality. Since a > 0, the parabola opens upward. Between the 2 real roots #(-3/4)# and (2), a part of the parabola is below the x-axis, meaning f(x) < 0.
Answer by open interval:# (-3/4, 2)#