Certainly! Here are some problems related to quadratic inequalities:

Problem 1

Solve the quadratic inequality: $x^2 - 4x - 5 > 0$

Problem 2

Solve the inequality and express the solution in interval notation: $3x^2 + 2x - 1 \leq 0$

Problem 3

Determine the set of values of $x$ that satisfies: $2x^2 - 8x + 6 < 0$

Problem 4

Solve the quadratic inequality: $x^2 + 6x + 9 \geq 0$

Problem 5

Find the values of $x$ that satisfy the following: $-2x^2 + 5x - 3 \geq 0$

---

Would you like detailed explanations or solutions to any of these problems?

Here are 5 related questions to explore:

1. How do you graph the solution set for a quadratic inequality?
2. What is the role of the discriminant in solving quadratic inequalities?
3. How do you apply the test point method in solving quadratic inequalities?
4. What happens when a quadratic inequality has no real solutions?
5. How do you solve quadratic inequalities with absolute values?

Tip: Always check the sign of the leading coefficient to determine the direction of the parabola when solving quadratic inequalities.