The image you provided shows a list of quadratic inequalities to be solved graphically. The heading says "Risolvere graficamente le seguenti disequazioni numeriche di secondo grado," which means "Solve graphically the following second-degree numerical inequalities." There are numbered problems (97 to 114) and their corresponding solutions or intervals of values where the inequality holds.

Here is a breakdown of some problems and their solutions:

Example Problems:

• 97: $x^2 - 5x + 4 > 0$

  • Solution: $x < 1$ or $x > 4$

• 99: $x^2 - 10x + 25 > 0$

  • Solution: $x \neq 5$ (the equation has a double root at 5, so inequality holds for all other values)

• 101: $x^2 - 64 \geq 0$

  • Solution: $x \leq -8$ or $x \geq 8$

• 109: $\frac{1}{2}x^2 + 6x > 0$

  • Solution: $0 < x < 12$

• 111: $3x^2 - 5 \geq 0$

  • Solution: $x \leq -\frac{\sqrt{5}}{3}$ or $x \geq \frac{\sqrt{5}}{3}$

Would you like further details on any of these problems, or assistance solving any specific inequality?

Relative Questions:

1. What is the graphical method for solving quadratic inequalities?
2. How do we determine the intervals where a quadratic inequality holds?
3. What are the common steps to solve $ax^2 + bx + c \leq 0$ inequalities algebraically?
4. How does the discriminant of a quadratic equation affect the solution of inequalities?
5. Can the solutions of quadratic inequalities be represented using set notation?

Tip:

Always check the sign of the leading coefficient when solving quadratic inequalities; it affects the direction of the inequality.