The quadratic case in practice

The following exercises are solved in this step.

We invite you to try to solve them before watching the video.

In any case, you will find below a PDF file with the solutions.

Exercise 1.

Solve the inequality [frac{3x-2}{2}<x^2 – 2.]

Exercise 2.

Solve the inequality [-x^2 + 6x – 9 > 0.]

Exercise 3.

Find the values of the parameter (k) for which the following inequality has solutions: [x^2 – kx – 20 leq 0.]

Exercise 4. [Solved only in the PDF file]

Find the values of the parameter (k) for which the following inequality is satisfied for any value outside the closed interval between two of its distinct roots: [2x^2 – 6x + k>0.]