If there is more than one root, enter additional roots with (OR)?

Question

Find all real or imaginary roots of

4x^2 + x + 3 = 0

Imaginary roots. Well, I have tried it this way:

there is no location for a plus or minus sign, I am trying to put thiis into a form that will allow the determination of x
if it is more than one, which it is, is the same equation written?

Answer 1

x = (-4 +/- sqrt(-47))/8
therefore the two roots are both imaginery.
x = (-4 +/- i*sqrt(47))/8

Answer 2

What way did you try?

Use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

with a=4, b=1, c=3:

x = (-1 +/- sqrt(1^2 - 48)) / 8 = (-1 +/- sqrt(-47)) / 8
= (-1/8) + (sqrt(47)/8)i, (-1/8) - (sqrt(47)/8)i

where i = sqrt(-1) is the imaginary unit.

Answer 3

Answer is:

-0.125 + 0.85696i
-0.125 - 0.85696i

Using the standard quadratic formula of:

x = (-b +/- sq. (b^2 -4ac))/2a

Where ax^2+bx=c=0 is the equation you are working with. In your case, a=a, b=1 and c= 3