Question

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

Answer 1

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)`