https://file.aiquickdraw.com/mathbot/file/1726005090141f99p51tq.jpg

The equation provided in the image is:

\[
x^2 - 5x + 3 = 0
\]

We will solve this using the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In this case, the coefficients are:
- \(a = 1\),
- \(b = -5\),
- \(c = 3\).

Let's calculate the discriminant and solve for \(x\).The roots of the equation \(x^2 - 5x + 3 = 0\) are approximately:

\[
x_1 = 4.30 \quad \text{and} \quad x_2 = 0.70
\]

None of the provided options match exactly because they are given in terms of square roots, so we need to convert the result back into the form provided in the answer choices. The discriminant is \(\sqrt{13}\), so let me adjust for that. 

The roots would be:

\[
x = \frac{5 \pm \sqrt{13}}{2}
\]

This corresponds to option **A** and option **D** in the image. Would you like more details on this?

Here are some related questions:

1. How does the discriminant affect the nature of the roots?
2. Can you explain how to derive the quadratic formula from completing the square?
3. What are the different methods to solve a quadratic equation besides the quadratic formula?
4. How can we factor quadratic equations that don't have real roots?
5. How does the quadratic formula handle complex roots?

**Tip:** Always check the discriminant \(b^2 - 4ac\) first to determine the type of solutions (real or complex).

Select the two values of x that are roots of the equation x^2 - 5x + 3 = 0.

Learn how to solve the quadratic equation x² - 5x + 3 = 0 step by step using the quadratic formula. This algebra problem involves calculating the discriminant and finding the roots, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation