The image you uploaded appears to contain a list of quadratic function problems, focused on finding the values of a parameter $m$ for which the given quadratic equation has two distinct real solutions. Each problem is accompanied by specific conditions or extra requirements for the solutions, such as finding solutions that satisfy certain inequalities or other given relationships.

Here are the key steps to solve these kinds of problems:

1. Determine the discriminant ($\Delta$): For a quadratic equation of the form $ax^2 + bx + c = 0$, the discriminant is given by: $\Delta = b^2 - 4ac$ For the equation to have two distinct real roots, the discriminant must be strictly positive: $\Delta > 0$

2. Apply the conditions given in the problem: Sometimes, the problems involve additional constraints, such as specific conditions on the roots (like one being larger than the other, or some relation between them). In those cases, you need to use the formulas for the sum and product of the roots, derived from Vieta's formulas:

   • The sum of the roots $x_1 + x_2 = -\frac{b}{a}$
   • The product of the roots $x_1 \cdot x_2 = \frac{c}{a}$

3. Solve for the parameter $m$: Once you have the discriminant and have applied any additional conditions, solve for the parameter $m$.

Would you like me to walk through a specific problem from the image or provide a detailed solution for one of them? Feel free to ask for clarification!

Here are 5 questions you could consider:

1. Would you like help solving the equation from 2024.12 or any other specific one from the image?
2. Do you need a deeper explanation on how to apply the discriminant condition for two distinct real roots?
3. Are you familiar with how to use Vieta’s formulas for the sum and product of roots, or should I explain further?
4. Would you like help understanding how to handle additional conditions, like inequalities related to the roots?
5. Should I assist with a graphical interpretation of quadratic functions?

Tip: When solving quadratic equations with parameters, always start by analyzing the discriminant to determine the nature of the roots.