SOLUTION: I have a problem and I have a solution too but don't understand one of the steps. This is the problem : (Sqrt(2) – 1) is a root of x2 + bx + c = 0, where b, c ∈ &#8484

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Question 1061041: I have a problem and I have a solution too but don't understand one of the steps.
This is the problem :
(Sqrt(2) – 1) is a root of x2 + bx + c = 0, where b, c ∈ ℤ. Find the value of b and the value of c and hence, find the other root.

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Try starting with factored form of a quadratic equation.
%28x-p%29%28x-v%29=0
and you have sqrt%282%29-1 as one of the roots. Maybe the other root is the conjugate of the known root? You might expect -sqrt%282%29-1., or -1-sqrt%282%29.

Let's see if working in reverse direction starting with the two roots.
%28x-%28-1%2Bsqrt%282%29%29%29%28x-%28-1-sqrt%282%29%29%29=0------will this work?

%28x%2B1-sqrt%282%29%29%28x%2B1%2Bsqrt%282%29%29=0
%28%28x%2B1%29-sqrt%282%29%29%28%28x%2B1%29%2Bsqrt%282%29%29=0, and recognize that give difference of squares;
%28x%2B1%29%5E2-%28sqrt%282%29%29%5E2=0
x%5E2%2B2x%2B1-2=0
x%5E2-2x-1=0 in which system%28a=1%2Cb=-2%2Cc=-1%29.

Both the given root and its conjugate are roots for this equation.

Your text book should also give a lesson on what happens when you determine the product of roots of a quadratic equation; and what happens when you take the sum of the roots of a quadratic equation.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

I have a problem and I have a solution too but don't understand one of the steps.
This is the problem :
(Sqrt(2) – 1) is a root of x2 + bx + c = 0, where b, c ∈ ℤ. Find the value of b and the value of c and hence, find the other root. 
Other root: highlight_green%28-+1+-+sqrt%282%29%29