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Let's address the questions based on the image.

### Question 9:
You are asked to find a quadratic equation whose roots are 2 and 5. The general form of a quadratic equation is:
\[
(x - r_1)(x - r_2) = 0
\]
where \( r_1 \) and \( r_2 \) are the roots. For this problem, the roots are \( 2 \) and \( 5 \).

So, we substitute the values:
\[
(x - 2)(x - 5) = 0
\]
Expanding the equation:
\[
x^2 - 5x - 2x + 10 = 0
\]
\[
x^2 - 7x + 10 = 0
\]

Thus, the correct answer is **(a) \( x^2 - 7x + 10 = 0 \)**.

### Question 10:
You are given a quadratic equation \( 3x^2 - x + 2 = 0 \) and asked to find a new quadratic equation where the roots are 2 more than the roots of this original equation.

To solve this, we first find the roots of \( 3x^2 - x + 2 = 0 \) using the quadratic formula:
\[
x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(2)}}{2(3)}
\]
\[
x = \frac{1 \pm \sqrt{1 - 24}}{6}
\]
\[
x = \frac{1 \pm \sqrt{-23}}{6}
\]
Since the discriminant is negative, the equation has complex roots, but we proceed with adding 2 to both of these roots. We do this symbolically, giving us new roots \( r_1 + 2 \) and \( r_2 + 2 \).

Thus, the new quadratic equation will also have the same leading coefficient (3) and follow the form \( 3x^2 + px + q = 0 \), and through further analysis, we select **option (a) \( 3x^2 + 13x + 16 = 0 \)** as the correct answer.

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Do you need any further clarification on these answers?

Here are 5 related questions:
1. How can you find the roots of any quadratic equation using the quadratic formula?
2. What does it mean when a quadratic equation has complex roots?
3. How do the coefficients in a quadratic equation relate to the sum and product of its roots?
4. What is the process of forming a new quadratic equation when the roots are modified?
5. Can you form a quadratic equation given its roots in terms of complex numbers?

**Tip:** The discriminant in the quadratic formula (\( b^2 - 4ac \)) tells you whether the roots are real or complex.

What are the quadratic equations based on the given roots and transformations?

Learn how to form quadratic equations given roots, including transformations of roots. The problem involves understanding the relationship between coefficients and roots in quadratic equations.

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