Solve Quadratic Equation for x1^2 + x2^2

In summary, the conversation discusses how to tướng find the value of x1^2 + x2^2 when given the roots of a quadratic equation. It is determined that the quadratic formula cannot be used since the equation has no real roots. Instead, Vieta's theorem is used to tướng find the sum and product of the roots, which can then be used to tướng find x1^2 + x2^2. The conversation also briefly touches on expanding (x1 + x2)^2 to tướng find the desired value.

Homework Statement

If the roots of x^2 - 2x + 4 = 0 are x1 and x2, what is x1^2 + x2^2?

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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.

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.

That's a good start.

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

How did you get to tướng that equation? :O

SammyS

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blunted said:

How did you get to tướng that equation? :O

Expand (x₁ + x₂)² & see what you get.

1. What is a quadratic equation?

A quadratic equation is a mathematical equation of the size ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The highest power of x in a quadratic equation is 2, making it a second-degree polynomial.

2. How bởi you solve a quadratic equation?

There are several methods for solving a quadratic equation, including factoring, completing the square, and using the quadratic formula. The most commonly used method is the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a.

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3. What is the discriminant of a quadratic equation?

The discriminant of a quadratic equation is the value inside the square root in the quadratic formula, b^2 - 4ac. It helps determine the nature of the solutions to tướng the equation. If the discriminant is positive, there are two distinct real solutions. If it is zero, there is only one real solution. And if it is negative, there are no real solutions.

4. Can a quadratic equation have more than thở two solutions?

No, a quadratic equation can have a maximum of two solutions. This is because a quadratic equation is a second-degree polynomial, which means it can have a maximum of two x-intercepts.

5. How bởi you graph a quadratic equation?

To graph a quadratic equation, you can use the coordinates of the x-intercepts (solutions) and the vertex of the parabola. The x-intercepts can be found by solving the equation for x, while the vertex can be found using the formula x = -b/2a and plugging that value into the equation to tướng find the y-coordinate.