https://file.aiquickdraw.com/mathbot/file/1729255100667hrbridq2.jpg

The equation in the image is:

\[
2x^2 - 7x - 4 = 0
\]

The question is asking for the **sum of the roots** of this quadratic equation.

For a general quadratic equation of the form \( ax^2 + bx + c = 0 \), the sum of the roots is given by the formula:

\[
\text{Sum of roots} = -\frac{b}{a}
\]

Here, the coefficients are:
- \( a = 2 \)
- \( b = -7 \)
- \( c = -4 \)

Using the formula for the sum of the roots:

\[
\text{Sum of roots} = -\frac{-7}{2} = \frac{7}{2}
\]

So, the sum of the roots of the equation \( 2x^2 - 7x - 4 = 0 \) is:

\[
\frac{7}{2}
\]

Would you like further details or explanations on this process?

Here are 5 related questions for further practice:
1. What is the product of the roots for the same equation?
2. How do you find the individual roots using the quadratic formula?
3. What happens to the sum of roots if the coefficient \( b \) is changed?
4. How can you verify the sum of roots using the actual solutions of the equation?
5. What is the significance of the sum of roots in a real-world application?

**Tip**: The sum and product of the roots of a quadratic equation are directly related to the coefficients \( b \) and \( a \), and they give insights into the properties of the quadratic without solving it directly!

Find the sum of the roots of the quadratic equation 2x^2 - 7x - 4 = 0.

Learn how to find the sum of roots for the quadratic equation 2x^2 - 7x - 4 = 0. This problem involves the formula for sum of roots, -b/a, and is ideal for students in Grades 9-10 studying algebra and 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