SOLUTION: Please help me solve this polynomial: ( n + 3 + 3n^2).

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Question 302244: Please help me solve this polynomial: ( n + 3 + 3n^2).
Found 2 solutions by london maths tutor, Alan3354:
Answer by london maths tutor(243) About Me  (Show Source):
You can put this solution on YOUR website!
3n%5E2+%2B+n+%2B+3
n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where a = 3, b = 1 and c = 3
n+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A3%2A3+%29%29%2F%282%2A3%29+

n+=+%28-1+%2B-+sqrt%28-35%29%29%2F%286%29+

n+=+%28-1+%2B-+%2835i%29%29%2F%286%29+%29


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B1x%2B3+=+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=%281%29%5E2-4%2A3%2A3=-35.

The discriminant -35 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 -35 is + or - sqrt%28+35%29+=+5.91607978309962.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B1%2Ax%2B3+%29