Understanding And Solving Quadratic Equations: 2X² + 7X + 15 = 0

Introduction

As a math teacher, it is important to understand and teach students about quadratic equations. Quadratic equations are equations that have the form ax² + bx + c = 0, where a, b, and c are constants. In this article, we will focus on solving the quadratic equation 2x² + 7x + 15 = 0.

Process for Solving

To solve this quadratic equation, we will use the quadratic formula, which is: x = (-b ± √(b² - 4ac)) / 2a We can plug in the values of a, b, and c from our equation 2x² + 7x + 15 = 0 to solve for x.

Step 1: Identify the Values of a, b, and c

In our equation 2x² + 7x + 15 = 0, a = 2, b = 7, and c = 15.

Step 2: Plug in the Values into the Quadratic Formula

Next, we plug in our values for a, b, and c into the quadratic formula: x = (-7 ± √(7² - 4(2)(15))) / 2(2)

Step 3: Simplify the Equation

Now we simplify the equation: x = (-7 ± √(49 - 120)) / 4 x = (-7 ± √(-71)) / 4

Step 4: Use Imaginary Numbers to Solve

Since we cannot take the square root of a negative number, we need to use imaginary numbers to solve for x. The square root of -71 is 8.426i, where i represents the imaginary unit. So our two solutions are: x = (-7 + 8.426i) / 4 or x = (-7 - 8.426i) / 4

Conclusion

In conclusion, the quadratic equation 2x² + 7x + 15 = 0 can be solved using the quadratic formula, which involves identifying the values of a, b, and c, plugging them into the formula, simplifying the equation, and using imaginary numbers to solve for x. As a teacher, it is important to teach students the steps for solving quadratic equations and provide them with opportunities to practice solving them on their own.