To solve the quadratic equation \( 2y^2 + 11x + 5 = 0 \) for \( y \) in terms of \( x \), we will use the quadratic formula: 

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

In this equation, the coefficients \( a \), \( b \), and \( c \) are taken from the standard quadratic form \( ay^2 + by + c = 0 \). Here, \( a = 2 \), \( b = 11x \), and \( c = 5 \).

1. Calculate the discriminant \( \Delta = b^2 - 4ac \):
   \[ \Delta = (11x)^2 - 4(2)(5) = 121x^2 - 40 \]

2. Substitute \( \Delta \), \( a \), and \( b \) back into the quadratic formula:
   \[ y = \frac{-(11x) \pm \sqrt{121x^2 - 40}}{2(2)} \]
   \[ y = \frac{-11x \pm \sqrt{121x^2 - 40}}{4} \]

Therefore, the solutions for \( y \) in terms of \( x \) are:
\[ y = \frac{-11x + \sqrt{121x^2 - 40}}{4} \]
\[ y = \frac{-11x - \sqrt{121x^2 - 40}}{4} \]

Do you want more details or have any questions?

Here are 8 related questions that expand on this information:

1. What is the value of \( y \) when \( x = 1 \)?
2. How do you find the roots of the quadratic equation \( 3y^2 + 4y - 2 = 0 \)?
3. What is the significance of the discriminant in the quadratic formula?
4. Can the quadratic formula be used to solve any quadratic equation?
5. How would you graph the quadratic function \( 2y^2 + 11x + 5 \) on a coordinate plane?
6. What happens to the roots if the discriminant is negative?
7. How do you complete the square to solve a quadratic equation?
8. What are the practical applications of solving quadratic equations in real life?

**Tip:** When solving quadratic equations, always simplify the coefficients as much as possible to make calculations easier.

Learn how to solve the quadratic equation 2y^2 + 11x + 5 = 0 for y in terms of x with a detailed step-by-step solution. This problem covers quadratic equations and the quadratic formula. Suitable for 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