### Math Notes

Subjects

#### High School Mathematics Solutions

##### Topics || Problems

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.