Which Of These Numbers Are Solutions Of $n^2 = 100$? Choose TWO Correct Answers.A. \[$-50\$\] B. \[$-25\$\] C. \[$-10\$\] D. 10 E. 25 F. 50

Introduction

In mathematics, quadratic equations are a fundamental concept that deals with solving equations of the form $ax^2 + bx + c = 0$. One of the most common types of quadratic equations is the equation $n^2 = k$, where $n$ is the variable and $k$ is a constant. In this article, we will focus on solving the equation $n^2 = 100$ and determine which of the given numbers are solutions to this equation.

Understanding the Equation $n^2 = 100$

The equation $n^2 = 100$ is a quadratic equation where the variable $n$ is squared and set equal to 100. To solve this equation, we need to find the values of $n$ that satisfy the equation. We can start by taking the square root of both sides of the equation.

Taking the Square Root of Both Sides

When we take the square root of both sides of the equation $n^2 = 100$, we get:

$$n = \pm \sqrt{100}$$

This equation tells us that $n$ is equal to the square root of 100, or $n$ is equal to the negative square root of 100.

Simplifying the Square Root

The square root of 100 is equal to 10, so we can simplify the equation as follows:

$$n = \pm 10$$

This equation tells us that $n$ is equal to 10 or $n$ is equal to -10.

Evaluating the Given Options

Now that we have solved the equation $n^2 = 100$, we can evaluate the given options to determine which of them are solutions to this equation.

• Option A: $-50$. This option is not a solution to the equation $n^2 = 100$ because $(-50)^2 = 2500$, which is not equal to 100.
• Option B: $-25$. This option is not a solution to the equation $n^2 = 100$ because $(-25)^2 = 625$, which is not equal to 100.
• Option C: $-10$. This option is a solution to the equation $n^2 = 100$ because $(-10)^2 = 100$.
• Option D: 10. This option is a solution to the equation $n^2 = 100$ because $10^2 = 100$.
• Option E: 25. This option is not a solution to the equation $n^2 = 100$ because $25^2 = 625$, which is not equal to 100.
• Option F: 50. This option is not a solution to the equation $n^2 = 100$ because $50^2 = 2500$, which is not equal to 100.

Conclusion

Introduction

In our previous article, we discussed solving the quadratic equation $n^2 = 100$ and determined which of the given numbers are solutions to this equation. In this article, we will address some frequently asked questions (FAQs) about solving quadratic equations.

Q: What is a quadratic equation?

A: A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. The general form of a quadratic equation is $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use various methods such as factoring, completing the square, or using the quadratic formula. The quadratic formula is a popular method for solving quadratic equations and is given by:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Q: What is the difference between a quadratic equation and a linear equation?

A: A linear equation is a polynomial equation of degree one, which means the highest power of the variable is one. The general form of a linear equation is $ax + b = 0$, where $a$ and $b$ are constants, and $x$ is the variable. Quadratic equations, on the other hand, have a degree of two, and their general form is $ax^2 + bx + c = 0$.

Q: Can I solve a quadratic equation by trial and error?

A: While it is possible to solve a quadratic equation by trial and error, it is not a recommended method. Trial and error can be time-consuming and may not always lead to the correct solution. Instead, use a more systematic approach such as factoring, completing the square, or using the quadratic formula.

Q: What is the significance of the discriminant in a quadratic equation?

A: The discriminant is the expression under the square root in the quadratic formula, which is $b^2 - 4ac$. The discriminant determines the nature of the solutions to the quadratic equation. If the discriminant is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one real solution. If the discriminant is negative, the equation has no real solutions.

Q: Can I solve a quadratic equation with complex coefficients?

A: Yes, you can solve a quadratic equation with complex coefficients. In fact, complex coefficients are a common occurrence in quadratic equations. To solve a quadratic equation with complex coefficients, you can use the quadratic formula and perform complex arithmetic.

Conclusion

In conclusion, solving quadratic equations is an essential skill in mathematics, and understanding the concepts and techniques involved can help you solve a wide range of problems. We hope this FAQ article has provided you with a better understanding of quadratic equations and how to solve them.

Additional Resources

• Quadratic Formula
• Factoring Quadratic Equations
• Completing the Square
• Quadratic Equations