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The image contains a series of mathematical questions and answers in Arabic, covering various topics such as solving equations, complex numbers, polynomial functions, and limits. I'll break down the first few problems and provide explanations for the key concepts involved.

1. **Question 7: Solve the quadratic equation**  
   \( x^2 - x - 20 = 0 \).  
   To solve this, we can use the quadratic formula:
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   where \( a = 1 \), \( b = -1 \), and \( c = -20 \). Solving this yields the discriminant:
   \[
   b^2 - 4ac = (-1)^2 - 4(1)(-20) = 1 + 80 = 81
   \]
   So,
   \[
   x = \frac{-(-1) \pm \sqrt{81}}{2(1)} = \frac{1 \pm 9}{2}
   \]
   The two solutions are:
   \[
   x = \frac{1 + 9}{2} = 5 \quad \text{and} \quad x = \frac{1 - 9}{2} = -4
   \]

   The correct answer is \( A = 5 \) and \( B = -4 \).

2. **Question 8: Find \( f(3) \) for the function \( f(x) = 3x^3 - 6x^2 + x - 11 \)**  
   Substituting \( x = 3 \) into the function:
   \[
   f(3) = 3(3^3) - 6(3^2) + 3 - 11 = 3(27) - 6(9) + 3 - 11
   \]
   \[
   = 81 - 54 + 3 - 11 = 19
   \]
   So the correct answer is \( A = 19 \).

3. **Question 9: Simplify \( (2 + 4i)(9 - 3i) \)**  
   Applying the distributive property:
   \[
   (2 + 4i)(9 - 3i) = 2(9 - 3i) + 4i(9 - 3i) = 18 - 6i + 36i - 12i^2
   \]
   Since \( i^2 = -1 \), we have:
   \[
   = 18 + 30i + 12 = 30 + 30i
   \]
   The correct answer is \( B = 30 + 30i \).

4. **Question 10: Classify the number \( a + bi \)**  
   - \( a + bi \) is a complex number if \( a \neq 0 \) and \( b \neq 0 \).  
   - If \( b = 0 \), it is a real number.  
   - If \( a = 0 \), it is an imaginary number.

   Thus, the options are:
   - Complex
   - Real
   - Imaginary

   The answer here is to determine if the given \( a + bi \) is complex or not.

5. **Question 12: Solve \( (x^2)^2 + 5(x^4) - 8 \)**  
   The expression simplifies as:
   \[
   (x^2)^2 = x^4
   \]
   Therefore, the expression becomes:
   \[
   x^4 + 5x^4 - 8 = 6x^4 - 8
   \]

Would you like detailed solutions for more questions? Here are 5 related questions to explore:

1. How do you solve quadratic equations with complex roots?
2. What are the different forms of complex numbers, and how are they classified?
3. How do you perform multiplication with complex numbers?
4. What is the importance of the discriminant in quadratic equations?
5. How can we solve higher-degree polynomials like quartic equations?

**Tip**: When multiplying complex numbers, remember to apply the distributive property and simplify using \( i^2 = -1 \).

Solve various mathematical problems involving quadratic equations, complex numbers, and limits.

This page provides detailed solutions to various mathematical problems, including quadratic equations, operations with complex numbers, and evaluating polynomial limits. These concepts are essential for students in Grades 10-12.

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