Solve the following polynomial inequality problem

Question

2x² +5x-3≤0

Answer 1

Let's first treat this like an equation

2x² + 5x - 3 = 0

(2x-1)(x+3) = 0

x = 1/2 & x = -3

Now let's look at the inequality again and test values to see which signs we should use

2x² + 5x - 3 ≤ 0

Let's say x = 1

2(1)² + 5(1) - 3 = 4 ≤ 0 -> False

Let's say x = -4

2(-4)² + 5(-4) - 3 = 9 ≤ 0 -> False

Therefore the answer is -3 ≤ x ≤ 1/2