Solve the inequality \(2x^2 -7x -4 \leq 0 \). Express your answer in interval notation.

Solution:

• \(2x^2 -7x -4 = 0 \)

• \(x_1 = \frac{--7+\sqrt{49-4(2)(-4)}}{2(2)} = 4\)

• \(x_1 = \frac{--7-\sqrt{49-4(2)(-4)}}{2(2)} = \frac{-1}{2}\)

• Answer: \([\frac{-1}{2},4]\). The values are from -0.5 to 4.