I’m trying to solve equations with the quadratic formula but keep getting answers that don’t work.
here is one:
x² + 2x + 5 = 0
when I use the quadratic formula I get -1 +/- 2i, which doesn’t work in the equation
what do I do?
+128406 x^2 + 2x + 5 = 0
Make sure we are using the correct values (and formula)
a = 1 b = 2 and c = 5
So we have
[ - b ±√ ( b^2 - 4ac) ]
________________ =
2a
[ -2 ±√ (2^2 - 4*1 * 5) ]
_________________ =
2*1
- 2 ±√ [4 - 20 ]
_____________ =
2
-2 ±√ (-16)
_________ =
2
-2 ± 4i
______ divide everything by 2
2
-1 ± 2i
Let's check this in the quadratic ...one root is 2i - 1
(2i - 1)^2 + 2 (2i - 1) + 5 =
(2i - 1) (2i - 1) + 2 (2i - 1) + 5
4i^2 - 4i + 1 + 4i - 2 + 5
- 4 + 1 - 2 + 5 =
-3 + 3 =
0
We don't need to check the other root....if one complex root makes a quadratic = 0, then its conjugate will, too !!!
