#3**0 **

Question: Solve the inequality \(4t^2 \le 9t-2\)

We rearrange it as follows:

\(4t^2-9t+2 \le 0\)

Then, factor this quadratic equation:

\((4t-1)(t-2) \le 0\)

The critical values (also called endpoints) are: \(t_1=\frac{1}{4},t_2=2\)

So, if we sketched the quadratic \(4t^2-9t+2\), it has x-intercepts (1/4 and 2).

And we want the region below the x-axis (As it is less than 0).

Hence, the region between 1/4 and 2.

Therefore: \(\frac{1}{4} \le t \le 2\)

Here is a sketch: (Using desmos.com)

I hope this helps.

Guest Jul 21, 2022

edited by
Guest
Jul 21, 2022