To determine the values of \( k \) for which a given equation has no solution, I would need the actual equation in question. However, as you have not provided the specific equation, I will discuss the general approach for different types of equations:
1. **Linear Equations**:
For a linear equation in one variable, such \( ax + b = 0 \), where \( a \) and \( b \) are constants, the equation always has a solution unless \( a = 0 \) and \( b \\eq 0 \), in which case the equation becomes inconsistent.
2. **Quadratic Equations**:
For a quadratic equation in the form \( ax^2 + bx + c = 0 \), we look at the discriminant \( D = b^2 - 4ac \). If \( D < 0 \), then there are no real solutions (the equation has no solution in real numbers, but might have complex solutions).
3. **Systems of Equations**:
In a system of linear equations, suppose we have two equations in the form:
\( \begin{align*}
a_1x + b_1y &= c_1, \\
a_2x + b_2y &= c_2.
\end{align*} \)
Such a system has no solution if the ratios of the coefficients are equal (\( \frac{a_1}{a_2} = \frac{b_1}{b_2} \)) but the ratio of the constants is not (\( \frac{c_1}{c_2} \\eq \frac{b_1}{b_2} \)). This indicates that the lines are parallel and will never intersect.
4. **Rational Equations**:
An equation involving rational expressions, such as \( \frac{a}{x-k} + b = 0 \), may have no solution if the denominator equals zero for any value of \( x \), causing a division by zero.
Since I don't have the specific equation you're referring to, I can't give you the exact values of \( k \) that will result in no solution. If you provide the equation in question, I would be able to offer a more targeted explanation and solution.