SOLUTION: Find all real or imaginary roots of 5x^2 + 5x + 4 = 0. (If there is more than one root, show additional roots

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Question 84871This question is from textbook Elementary and intermediate Algebra
: Find all real or imaginary roots of 5x^2 + 5x + 4 = 0.
(If there is more than one root, show additional roots
This question is from textbook Elementary and intermediate Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We can find the roots of this quadratic with the quadratic formula

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B5x%2B4+=+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=%285%29%5E2-4%2A5%2A4=-55.

The discriminant -55 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 -55 is + or - sqrt%28+55%29+=+7.41619848709566.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B5%2Ax%2B4+%29



So the quadratic has two imaginary roots

x=5%2Bi%2Asqrt%2811%29%2F2 or x=5-i%2Asqrt%2811%29%2F2