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### Question 2:
It involves two quadratic equations, with \( p \) as a variable parameter:

1. \( x^2 + p x + 4 = 0 \)
2. \( x^2 + 4p x + p = 0 \)

#### Part (1): 
You are asked to analyze the equations to determine the values of \( p \) for which the real solutions exist and explore how those solutions vary with \( p \).

#### Part (2):
You are asked to eliminate one variable, likely combining the two equations to derive additional conditions on \( p \).

#### Part (3):
This part involves the discriminant of the quadratic equations, which helps in determining the conditions for real solutions based on \( p \)'s value.

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Here are some related questions you could explore:

1. How do we calculate the discriminant of a quadratic equation?
2. What does it mean when the discriminant is positive, negative, or zero?
3. How can we solve for the roots of a quadratic equation using the quadratic formula?
4. What conditions ensure that two quadratic equations have real roots?
5. How can you apply Vieta’s formulas to relate the coefficients and roots?

**Tip**: The discriminant \( \Delta = b^2 - 4ac \) helps determine the nature of roots for quadratic equations.

Solve two quadratic equations (1) x^2 + p x + 4 = 0 and (2) x^2 + 4p x + p = 0. Determine the range of p where the equations have real solutions and combine them for further analysis.

Explore how to solve two quadratic equations x^2 + p x + 4 = 0 and x^2 + 4p x + p = 0. Learn to calculate the discriminant to determine real solutions and analyze the range of p for different cases.

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