SAT Question 1ce9ffcd: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice A is incorrect. If the value of $c$ is $3$, this would yield a discriminant that is greater than zero. Therefore, the given equation would have two solutions, rather than exactly one solution.

Choice B is incorrect. If the value of $c$ is $0$, this would yield a discriminant that is greater than zero. Therefore, the given equation would have two solutions, rather than exactly one solution.

Choice D is incorrect. If the value of $c$ is $-53$, this would yield a discriminant that is less than zero. Therefore, the given equation would have no real solutions, rather than exactly one solution.