2x^3+9x^2-5x>0

Question

to solve the inequality, graphing and interval notation

Answer 1

Step 1. Factor 2x^3+9x^2-5x > 0

=> x(2x^2+9x-5) = x(2x-1)(x+5) > 0

Step 2. Find boundary points: x = -5, 0, 1/2

Step 3. Check intervals: (-oo, -5), (-5, 0), (0, 1/2) and (1/2, oo)

Step 4. Write answer: (-5, 0) U (1/2, oo)

Answer 2

Start by factoring and getting the roots of the polynomial.

2x³ + 9x² - 5x > 0

(2x²+9x-5)x > 0

(2x-1)(x+5)x > 0

Roots in increasing order: x=-5, x=0, x=1/2

By graphing, we see the solution set consist of two intervals,

-5 < x < 0 and x > 1/2

in interval notation, x belongs to (-5,0) U (1/2,∞)

 

You can also get the intervals by seeing when there are an even number of factors with negative value.