how to find roots of -9 and 0 using formula of x² -(sum) + (product)=0​​​​​​

To find the quadratic equation with roots using the formula \( x^2 - (\text{sum of the roots})x + (\text{product of the roots}) = 0 \), let's break down the problem step by step for the roots \( -9 \) and \( 0 \).

### Steps:

1. **Find the sum of the roots:**
   \[
   \text{Sum of roots} = -9 + 0 = -9
   \]

2. **Find the product of the roots:**
   \[
   \text{Product of roots} = -9 \times 0 = 0
   \]

3. **Substitute the sum and product into the formula \( x^2 - (\text{sum})x + (\text{product}) = 0 \):**

   Now, substitute the values into the formula:
   \[
   x^2 - (\text{sum of the roots})x + (\text{product of the roots}) = 0
   \]
   \[
   x^2 - (-9)x + 0 = 0
   \]

4. **Simplify the equation:**
   \[
   x^2 + 9x = 0
   \]

Thus, the quadratic equation with roots \( -9 \) and \( 0 \) is:
\[
x^2 + 9x = 0
\]

This matches the equation we found earlier. The formula \( x^2 - (\text{sum of roots})x + (\text{product of roots}) = 0 \) provides a straightforward way to generate the quadratic equation when the roots are known.

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### Related Questions:
1. How does factoring work when one of the roots is zero?
2. What is the relation between the discriminant and the type of roots in a quadratic equation?
3. How can you graph a quadratic equation based on its roots?
4. How do you derive the quadratic formula from the standard form of a quadratic equation?
5. Can you solve a quadratic equation by completing the square?
6. What happens when both roots are the same?
7. What is the axis of symmetry for a quadratic equation with known roots?
8. How do you solve a quadratic equation when the roots are complex numbers?

### Tip:
When one of the roots is zero, the quadratic equation will always be factorable as \( x(x + r) = 0 \), where \( r \) is the non-zero root.

Learn how to find the roots of -9 and 0 using the quadratic equation formula x^2 + 9x = 0. This detailed solution covers step-by-step calculations for sum of roots, product of roots, and simplifying the quadratic equation. Suitable for students in Grades 7-9.

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