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?

Guest Nov 19, 2018

#1**+1 **

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 !!!

CPhill
Nov 19, 2018