SOLUTION: Solve the following quadratic equation by the quadratic formula. Simplify the solutions and write them in a + bi form. Answers in comma-separated list. X square + 2x + 5 =0

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Solve the following quadratic equation by the quadratic formula. Simplify the solutions and write them in a + bi form. Answers in comma-separated list. X square + 2x + 5 =0      Log On


   

Question 988542: Solve the following quadratic equation by the quadratic formula. Simplify the solutions and write them in a + bi form. Answers in comma-separated list.
X square + 2x + 5 =0
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
x%5E2%2B2x%2B5=0
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A5=-16.

The discriminant -16 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -16 is + or - sqrt%28+16%29+=+4.

The solution is x%5B12%5D+=+%28-2%2B-+i%2Asqrt%28+-16+%29%29%2F2%5C1+=++%28-2%2B-+i%2A4%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B5+%29

ANSWER: -1+2i, -1-2i