The Equation 3X<Sup>2</Sup> + 5X + 10: Explanation And Solution

Solved Solve using the quadratic formula 3x^2 5x 1 = 0 from www.chegg.com

Introduction

As a professional teacher, it is my duty to provide an explanation and solution to the given equation which is 3x² + 5x + 10. This equation is a quadratic equation because it has a degree of 2.

Understanding Quadratic Equations

A quadratic equation is an equation that can be written in the form of ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The highest power of the variable in a quadratic equation is 2.

Explanation of the Equation

In the equation 3x² + 5x + 10, a = 3, b = 5, and c = 10. This means that this equation is a quadratic equation with a coefficient of 3 for the x² term, a coefficient of 5 for the x term, and a constant of 10.

The Solution

To solve this equation, we can use the quadratic formula which is x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values of a, b, and c in the equation we get x = (-5 ± sqrt(5² - 4(3)(10))) / 2(3).

Calculating the Solution

Using the order of operations, we first calculate the value inside the square root which is 5² - 4(3)(10) = -95. Since the value inside the square root is negative, the equation has no real solutions.

Interpreting the Solution

This means that the quadratic equation 3x² + 5x + 10 has no real solutions, which implies that the graph of the equation does not intersect the x-axis. The graph is a parabola that opens upwards because the coefficient of the x² term is positive.

Conclusion

In conclusion, the equation 3x² + 5x + 10 is a quadratic equation with no real solutions. The quadratic formula was used to solve the equation, but the value inside the square root was negative, indicating that the equation has no real solutions. Understanding quadratic equations is important in mathematics, especially in algebra and calculus.