https://file.aiquickdraw.com/mathbot/file/17261586155064jbzam9w.jpg

The problem statement in the image is in Dutch and involves a quadratic equation. Here's the translation and the problem statement:

**Problem:**
If \( x_1 \) and \( x_2 \) are the roots of the equation \( x^2 + 5x - 3 = 0 \), calculate the value of \( \frac{1}{x_1} + \frac{1}{x_2} \) without finding the roots themselves.

**Solution:**

Given the quadratic equation:

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

The sum and product of the roots \( x_1 \) and \( x_2 \) can be found using Vieta's formulas:

1. **Sum of the roots**: \( x_1 + x_2 = -\frac{b}{a} = -\frac{5}{1} = -5 \).
2. **Product of the roots**: \( x_1 \cdot x_2 = \frac{c}{a} = \frac{-3}{1} = -3 \).

We need to calculate:

\[
\frac{1}{x_1} + \frac{1}{x_2}
\]

This can be rewritten as:

\[
\frac{1}{x_1} + \frac{1}{x_2} = \frac{x_1 + x_2}{x_1 \cdot x_2}
\]

Substituting the values we found:

\[
\frac{1}{x_1} + \frac{1}{x_2} = \frac{-5}{-3} = \frac{5}{3}
\]

So, the value of \( \frac{1}{x_1} + \frac{1}{x_2} \) is \( \frac{5}{3} \).

Would you like more details, or do you have any questions?

Here are some related questions you might find interesting:

1. How do you find the roots of a quadratic equation using the quadratic formula?
2. What are Vieta's formulas, and how are they used to solve problems involving roots?
3. Can Vieta's formulas be applied to polynomials of higher degrees?
4. How would the solution change if the coefficients of the equation were complex numbers?
5. How can we find other expressions involving the roots without solving for the roots directly?

**Tip:** Vieta's formulas are powerful tools that can help you solve problems involving the sums and products of polynomial roots without solving for the roots directly!

If x1 and x2 are the roots of the equation x^2 + 5x - 3 = 0, calculate the value of (1/x1) + (1/x2) without finding the roots themselves.

Learn how to calculate the reciprocal sum of roots (1/x1) + (1/x2) of the quadratic equation x^2 + 5x - 3 = 0 using Vieta's Formulas. This guide covers key algebraic concepts and is suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation