For what values of k does the equation
- x + k = 0 have no real roots

The equation \(-x + k = 0\) is a linear equation in the form of \(ax + b = 0\), where \(a = -1\) and \(b = k\).

To determine when this equation has no real roots, let's analyze it:

1. **Rearrange the equation**: 
   \[
   -x + k = 0
   \]
   \[
   x = k
   \]

2. **Interpretation**:
   - This equation suggests that \(x = k\). 
   - A linear equation like this always has exactly one solution (i.e., one real root) unless the equation is contradictory.

Since the equation is linear and always results in a valid \(x\) for any real value of \(k\), it will always have exactly one real root. Therefore, there are **no values of \(k\)** that would cause the equation \(-x + k = 0\) to have no real roots.

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. What values of \(k\) cause a quadratic equation to have no real roots?
2. How do you determine the number of real roots of a quadratic equation?
3. How does the discriminant of a quadratic equation relate to the number of real roots?
4. Can a linear equation have no real roots? Why or why not?
5. What is the general form of a linear equation, and how many roots does it have?
6. How can a linear equation be graphically represented, and what does the graph tell us about the roots?
7. What is the difference between a linear and a quadratic equation in terms of roots?
8. How does the slope of a line in a linear equation affect the roots?

**Tip:** Always analyze the form of the equation first to determine the type of solutions it may have!

Explore the conditions under which the linear equation x + k = 0 has no real roots. Learn about linear equations, real roots, and how different values of k affect the nature of solutions. Suitable for Grades 7-9 students studying algebra.

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