Question #N702
The equation $x^2-2x+k=0$ 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 when its discriminant is equal to zero. The discriminant of the quadratic equation $ax^2 + bx + c = 0$ is $b^2 - 4ac$. For the given equation, $a = 1$, $b = -2$, and $c = k$. Setting the discriminant equal to zero, we get $(-2)^2 - 4(1)(k) = 0$, or $4 - 4k = 0$. Solving for $k$ yields $k = 1$.