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Solve the equation $x^{2} - 4x + 4 = 0$. What is the nature of the solutions?

What is the discriminant of the quadratic equation $2x^{2} + 3x + 5 = 0$ and what does it indicate about the solutions?

For the equation $x^{2} + 2x + 1 = k$, determine the values of $k$ for which the equation has two solutions.

Identify the number of solutions for the quadratic equation $3x^{2} + 6x + 9 = 0$.

What are the solutions to the equation $x^{2} + 4x + 4 = 0$?

If the quadratic $x^{2} - 10x + 25 = k$ has no solutions, what is the range of values for $k$?

What type of solutions does the equation $x^{2} + 1 = 0$ have?

For the quadratic equation $x^{2} + 6x + 10 = 0$, how many solutions exist?

Which of the following values of $k$ will ensure the quadratic equation $x^{2} - 4x + k = 0$ has exactly one solution?

The equation $x^{2} + 3x + 2 = 0$ can be factored as $(x + a)(x + b) = 0$. What are the values of $a$ and $b$?