SOLUTION: Find all real or imaginary solutions to each equation. Use the method of your choice. w^2=-225 and 3v^2+4v-1=0

Question 78127: Find all real or imaginary solutions to each equation. Use the method of your choice.
w^2=-225
and
3v^2+4v-1=0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
For each of these problems it's easiest to use the quadratic formula (since there are going to be complex roots):

Add 225 to both sides
Now lets use the quadratic formula:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -900 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 -900 is + or - .

The solution is

Here's your graph:

So we have 2 complex (or imaginary) solutions:
or
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Again lets use the quadratic formula:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=28 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.21525043702153, -1.54858377035486. Here's your graph:

So we have 2 real solutions:
or
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