SOLUTION: Determine a quadratic equation with integer coefficients that has roots -1+-4sqrt2/2. Can someone please help explain this to me ?

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Question 119093: Determine a quadratic equation with integer coefficients that has roots -1+-4sqrt2/2. Can someone please help explain this to me ?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Determine a quadratic equation with integer coefficients that has roots
%28-1+%2B-++4sqrt%282%29%29%2F2. Can someone please help explain this to me ?

You have to know this fact:
If the quadratic equation:

x² + bx + c = 0

has roots r1 and r2, then b = -(r1 + r2) and c = r1r2

So if the quadratic equation:

x² + bx + c = 0

is to has roots r1 = %28-1%2B4sqrt%282%29%29%2F2 and r2 = %28-1-4sqrt%282%29%29%2F2,
then b = -(r1 + r2) = -%28%28-1%2B4sqrt%282%29%29%2F2+%2B+%28-1-4sqrt%282%29%29%2F2%29 =

-%28%28-1%2B4sqrt%282%29-1-4sqrt%282%29%29%2F2%29 =

-%28-1-1%29%2F2 = -%28-2%29%2F2 = -%28-1%29 = 1

and c = r1r2 =  %28%28-1%2B4sqrt%282%29%29%2F2%29%28%28-1-4sqrt%282%29%29%2F2%29 = 
%28-1%2B4sqrt%282%29%29%28-1-4sqrt%282%29%29%2F4 = %281%2B4sqrt%282%29-4sqrt%282%29-16sqrt%284%29%29%2F4 =
%281-16%282%29%29%2F4 = %281-32%29%2F4 = %28-31%29%2F4 = -31%2F4

So the equation

x² + bx + c = 0

becomes

x² + 1x + %28-31%2F4%29 = 0

But that doesn't have integer coefficients, so we clear of
fractions so it will:

So we multiply every term by LCD = 4

4x² + 4x + 4%28-31%2F4%29 = 0

4x² + 4x - 31 = 0 

Now that one has only integer coefficients.

Edwin