Turn this into quadratic equation -2/3 and 3/4

To turn the fractions \(-\frac{2}{3}\) and \(\frac{3}{4}\) into a quadratic equation, we need to use these values as the roots of the quadratic equation. If \(x_1\) and \(x_2\) are the roots, then the quadratic equation can be written as:

\[
(x - x_1)(x - x_2) = 0
\]

Substituting the roots:

\[
(x + \frac{2}{3})(x - \frac{3}{4}) = 0
\]

Now, let's simplify this equation.

First, expand the expression:

\[
x^2 - \frac{3}{4}x + \frac{2}{3}x - \frac{2}{3} \times \frac{3}{4} = 0
\]

Next, combine like terms and simplify:

\[
x^2 + \left(\frac{2}{3} - \frac{3}{4}\right)x - \frac{6}{12} = 0
\]

Simplifying further:

\[
x^2 - \frac{1}{12}x - \frac{1}{2} = 0
\]

The quadratic equation that has \(-\frac{2}{3}\) and \(\frac{3}{4}\) as roots is:

\[
x^2 - \frac{1}{12}x - \frac{1}{2} = 0
\]

Do you want more details or have any questions?

Here are five related questions to expand your understanding:
1. How do you find the sum of the roots of a quadratic equation?
2. What is the significance of the discriminant in a quadratic equation?
3. How can you factorize a quadratic equation?
4. How do you complete the square to solve a quadratic equation?
5. What are the real-world applications of quadratic equations?

**Tip:** When dealing with fractions in quadratic equations, it's helpful to first clear the fractions by multiplying through by the least common denominator.

Turn this into a quadratic equation: -2/3 and 3/4

Learn how to form a quadratic equation from the given roots -2/3 and 3/4. Understand key algebraic concepts such as forming quadratic equations from roots, expanding expressions, and simplifying fractions. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation