Quadratic Equations Help?

Question

The problem I got was x²-2x+26=0 and the answer ended up being [1+5i,1-5i]. I don't understand how it up being that.

Answer 1

Some of the reasoning behind the answers given: They are totally correct. When there is a negative under the radical you can get rid of it simply by taking an i and putting it outside the radical. 

 

√(-10) = i√(10)

 

That's why when it is √(4-104) it turns into √(-100) and then (i)(√(100)) and then 10i, since 10 times 10 is 100.

 

Answer 2

quadratic formula:  (-b ±√(b²-4ac))/2a

 

a=1    b=-2    c=26    gives:

 

(2 ±√4-4x1x26)/2   =

 

 (2±√(4-104))/2   =

 

 

2/2  ±(√-100)/2    =

 

1 ±10i/2    =

 

. 1 + 5i and 1-5i

Answer 3

One way to solve quadratic equation is using the Quadratic Formula.

In the problem, x²-2x+26=0, 

a=1

b=-2

c=26

 

Now plug these in the QE, x=[ -b ±√(b²-4ac)]/2a; then simplify.

 

x=[ -(-2)±√(-2)²-4(1)(26)]/2(1)

 

 =[2±√(4-104)]/2

 

x=[2+10i]/2      Or           x=[2-10i]/2

x=1+5i.            Or            x=1-5i