solve the inequality in interval notation 4x 3 >11x 2 +20x Solution 4x^3 > 11x^2

Question

solve the inequality in interval notation
4x3>11x2+20x

Explanation / Answer

4x^3 > 11x^2 + 20x [put in standard form] 4x^3 - 11x^2 - 20x > 0 [factor out an x] x(4x^2 - 11x - 20) > 0 [factor the quadratic] x(4x+5)(x-4) > 0 [make into equation] x(4x+5)(x-4) = 0 [find the critical numbers] x = 0, x = -5/4, x = 4 pick values in each region and test whether true/false less than -5/4: x = -10 [fails] between -5/4 and 0: x = -1 [passes] between 0 and 4: x = 2 [fails] larger than 4: x = 5 [passes] solution: (-5/4, 0) U (4, infinity)

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