There are 5 quadratics below. Four of them have two distinct roots each. The other has only one distinct root; find the value of that root.
4x^2 + 16x + 8
-x^2 + 4x + 5
9x^2 - 6x + 1
2x^2 - 8x + 4
225x^2 - 30x + 9
+1224 Find the discriminant (b^2 - 4ac) and see which equation has a discriminant of 0.
4x^2 + 16x + 8 ---> 16^2 - 4(4)(8) = 128
-x^2 + 4x + 5 ---> 4^2 - 4(-1)(5) = 36
9x^2 - 6x + 1 ---> (-6)^2 - 4(9)(1) = 0
We know that only one quadratic has one distinct root, so we can stop checking here.
9x^2 - 6x + 1 = 0
(3x - 1)^2 = 0
3x - 1 = 0
x = 1/3
