SOLUTION: My math question reads: If one of the solutions to a quadratic function is 1+i(squareroot2), what is the b value in the quadratic polynomial? Could you please help me figure out

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: My math question reads: If one of the solutions to a quadratic function is 1+i(squareroot2), what is the b value in the quadratic polynomial? Could you please help me figure out       Log On


   

Question 176400: My math question reads:
If one of the solutions to a quadratic function is 1+i(squareroot2), what is the b value in the quadratic polynomial?
Could you please help me figure out this math problem?
Please and thank you.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-%281%2Bisqrt%282%29%29%29%28x-%281-isqrt%282%29%29%29since 1%2Bsqrt%282%29} and 1-sqrt%282%29are factors
:
%28x-1-isqrt%282%29%29%28x-1%2Bisqrt%282%29%29
:
x%5E2-x%2Bisqrt%282%29x-x%2B1-isqrt%282%29-isqrt%282%29x%2Bisqrt%282%29-i%5E2%282%29
:
x%5E2-2x%2B3collecting all like terms
:
b=-2
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%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=%28-2%29%5E2-4%2A1%2A3=-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+1%2Ax%5E2%2B-2%2Ax%2B3+%29