Solve Quadratic Equation for x1^2 + x2^2

[blunted]

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.

 

[Mark44]

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.

That's a good start.

x₁² + x₂² = (x₁ + x₂)² - 2x₁x₂, right?

 

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How did you get to that equation? :O

 

[SammyS]

How did you get to that equation? :O

Expand (x₁ + x₂)² & see what you get.

 

[blunted]

Oh, right.. Thanks!