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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
avatar+92785 
+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 !!!

 

 

cool cool cool

CPhill  Nov 19, 2018

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