Question

Which of the following equations has only one solution?

a) x^2 = 9
b) x(x - 1) = 9
c) x^2 - 6x + 9 = 0

Answer 1

C has only one solution.
A is solved by taking the square root of both sides, which gives x= 3 or -3
B can be rewritten in quadratic form, giving x^2-x-9=0, and the solutions after a bit of work are 1/2(1+/- sqrt(37))
But the hard work of B can be skipped by factoring C, which factors to (x-3)^2 or x=3

Answer 2

edit- B's solutions are, to be precise: \[(1/2)(1\pm \sqrt{37})\]

Answer 3

you can also check the discriminant which is b^2-4ac and if it equals 0 it has one solution