SOLUTION: Find the solution set in a +bi form: 6x^2 + 4x +1 =0 I tried and here is what I have so far then I'm lost. Use the quadratic equation. The constants are a=6, b=4 and c=1.

Algebra ->  Trigonometry-basics -> SOLUTION: Find the solution set in a +bi form: 6x^2 + 4x +1 =0 I tried and here is what I have so far then I'm lost. Use the quadratic equation. The constants are a=6, b=4 and c=1.       Log On


   



Question 411559: Find the solution set in a +bi form: 6x^2 + 4x +1 =0
I tried and here is what I have so far then I'm lost.
Use the quadratic equation. The constants are a=6, b=4 and c=1.
x = -b +/-sqrt(b^2-4ac)]/12
Thank you so much

Found 2 solutions by ewatrrr, Alan3354:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
Finding the solution set in a +bi form:
6x^2 + 4x +1 =0
a=6, b=4 and c=1 |Yes!
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x = -b ± sqrt(b^2-4ac)]/12 |Yes! Finish substituting for b, b^2 and 4ac
x = -4 ± sqrt(16-24)]/12
x = -4 ± sqrt(-8)]/12
x = -4 ± sqrt(-1*4*2)]/12 |sqrt(-1) = i
x = -4 ± 2isqrt(2)]/12
x = -1/3 ± (1/6)isqrt(2)
x = -1/3 + (1/6)isqrt(2) x = -1/3 - (1/6)isqrt(2)

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 6x%5E2%2B4x%2B1+=+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=%284%29%5E2-4%2A6%2A1=-8.

The discriminant -8 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 -8 is + or - sqrt%28+8%29+=+2.82842712474619.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B4%2Ax%2B1+%29

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