https://r2.erweima.ai/mathbot/image/1726708746768kcv4xzxc.jpg

The equation presented in the image is:

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

You are asked to find the sum (和) and product (積) of the two solutions to this quadratic equation.

To solve this, we can use Vieta's formulas for a quadratic equation of the form \( ax^2 + bx + c = 0 \). According to Vieta's formulas:

1. The sum of the roots is given by:
   \[
   \text{Sum} = -\frac{b}{a}
   \]
2. The product of the roots is given by:
   \[
   \text{Product} = \frac{c}{a}
   \]

Here, \( a = 1 \), \( b = -5 \), and \( c = 3 \).

- The sum of the roots is:
  \[
  \text{Sum} = -\frac{-5}{1} = 5
  \]
- The product of the roots is:
  \[
  \text{Product} = \frac{3}{1} = 3
  \]

Thus:
- The sum (和) is \( 5 \),
- The product (積) is \( 3 \).

Let me know if you'd like more details or have any questions!

---

Here are 5 related questions for further practice:
1. What are the individual solutions to \( x^2 - 5x + 3 = 0 \)?
2. How would you factor \( x^2 - 5x + 3 = 0 \)?
3. How do Vieta's formulas apply to a general quadratic equation?
4. Can you derive the quadratic formula from a general quadratic equation?
5. What is the discriminant of the quadratic equation, and what does it tell you about the solutions?

**Tip:** Vieta's formulas are a quick way to find the sum and product of the roots of a quadratic equation without solving for the roots explicitly.

Find the sum and product of the roots of the quadratic equation x^2 - 5x + 3 = 0.

Explore how to find the sum and product of the roots for the equation x^2 - 5x + 3 = 0 using Vieta's formulas. This guide provides insights into algebraic principles and demonstrates practical applications of these formulas. Ideal for high school students learning quadratic equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation