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 ∈ ℤ
Algebra.Com
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(39617) (Show Source): You can put this solution on YOUR website!
Try starting with factored form of a quadratic equation.
and you have as one of the roots. Maybe the other root is the conjugate of the known root? You might expect ., or .
Let's see if working in reverse direction starting with the two roots.
------will this work?
, and recognize that give difference of squares;
in which .
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) (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:
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