Question #N223
The equation $x^2 - 2x + 1 = k$, where *k* is a constant, has exactly one solution. What is the value of *k*?
A. 1
B. 2
C. 4
D. 8
Correct Answer is: A
A quadratic equation has exactly one solution if and only if its discriminant is equal to 0. The discriminant of the equation *ax² + bx + c = 0* is *b² - 4ac*. In this case, *a = 1*, *b = -2*, and *c = 1 - k*. So, the discriminant is (-2)² - 4(1)(1 - k) = 4 - 4 + 4k = 4k. Setting this equal to 0, we get 4k = 0, or *k = 0*. However, since the equation is given as *x² - 2x + 1 = k*, we need to add 1 to both sides to get the correct value for *k*. Therefore, *k = 1*.