The discussion revolves around finding the value of x1^2 + x2^2 given the quadratic equation x^2 - 2x + 4 = 0, where x1 and x2 are the roots. The problem is situated within the context of quadratic equations and their properties.
The discussion is active, with participants building on each other's contributions. One participant has suggested a formula for x1^2 + x2^2, prompting questions about its derivation, indicating a collaborative exploration of the mathematical reasoning involved.
There is a recognition that the quadratic equation does not have real roots, which influences the approach to the problem. The discussion also reflects on the use of Vieta's theorem and the implications of complex numbers in the context of the problem.
blunted said:Homework Statement
If the roots of x^2 - 2x + 4 = 0 are x1 and x2, what is x1^2 + x2^2?
Homework Equations
The Attempt at a Solution
I don't think these questions can be answered by solving for x only cause there will be no real root(complex number).
So I found that x1 + x2 = 2 and x1 * x2 = 4 via Vieta's theorem.
And I tried solving it with the quadratic formula but as I said it hasn't got a real root.
Expand (x1 + x2)2 & see what you get.blunted said:How did you get to that equation? :O