Solve For Y Y Y . 5 Y 2 − 20 Y = 0 5y^2 - 20y = 0 5 Y 2 − 20 Y = 0 If There Is More Than One Solution, Separate Them With Commas. If There Is No Solution, Click On No Solution. Y = Y = Y = _______ \sqrt{\ } ​ No Solution.

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Introduction

Quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving the quadratic equation $5y^2 - 20y = 0$. We will break down the solution process into manageable steps, making it easy for readers to understand and follow along.

Understanding the Equation

The given equation is a quadratic equation in the form of $ay^2 + by + c = 0$, where $a = 5$, $b = -20$, and $c = 0$. To solve this equation, we need to find the values of $y$ that satisfy the equation.

Factoring the Equation

One way to solve quadratic equations is by factoring. We can start by factoring out the greatest common factor (GCF) of the terms. In this case, the GCF is $5y$. Factoring out $5y$ gives us:

$$5y^2 - 20y = 5y(y - 4) = 0$$

Setting Each Factor Equal to Zero

Now that we have factored the equation, we can set each factor equal to zero and solve for $y$. This gives us two separate equations:

$$5y = 0 \quad \text{and} \quad y - 4 = 0$$

Solving for $y$

We can solve each equation separately. Starting with the first equation, we have:

$$5y = 0 \Rightarrow y = 0$$

This gives us one solution for $y$. Moving on to the second equation, we have:

$$y - 4 = 0 \Rightarrow y = 4$$

This gives us another solution for $y$.

Combining the Solutions

Since we have found two separate solutions for $y$, we can combine them by separating them with commas. Therefore, the solutions to the equation $5y^2 - 20y = 0$ are:

$$y = 0, 4$$

Conclusion

In this article, we have solved the quadratic equation $5y^2 - 20y = 0$ using the method of factoring. We have found two solutions for $y$, which are $y = 0$ and $y = 4$. By following the steps outlined in this article, readers should be able to solve similar quadratic equations with ease.

Frequently Asked Questions

• What is a quadratic equation? A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. It is typically written in the form of $ay^2 + by + c = 0$.
• How do I solve a quadratic equation? There are several methods to solve quadratic equations, including factoring, using the quadratic formula, and graphing. In this article, we have used the method of factoring.
• What is the quadratic formula? The quadratic formula is a formula that can be used to solve quadratic equations. It is given by:

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

Additional Resources

For more information on solving quadratic equations, readers can refer to the following resources:

• Khan Academy: Solving Quadratic Equations
• Mathway: Solving Quadratic Equations
• Wolfram Alpha: Solving Quadratic Equations

Final Answer

The final answer is: $\boxed{0, 4}$

Introduction

Quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In our previous article, we provided a step-by-step guide on how to solve quadratic equations using the method of factoring. In this article, we will answer some of the most frequently asked questions about solving quadratic equations.

Q&A

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. It is typically written in the form of $ay^2 + by + c = 0$.

Q: How do I solve a quadratic equation?

A: There are several methods to solve quadratic equations, including factoring, using the quadratic formula, and graphing. In our previous article, we used the method of factoring.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that can be used to solve quadratic equations. It is given by:

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

Q: When should I use the quadratic formula?

A: You should use the quadratic formula when the equation cannot be factored easily or when the equation is in the form of $ax^2 + bx + c = 0$.

Q: How do I use the quadratic formula?

A: To use the quadratic formula, you need to plug in the values of $a$, $b$, and $c$ into the formula. Then, simplify the expression and solve for $y$.

Q: What is the difference between the quadratic formula and factoring?

A: The quadratic formula is a general method for solving quadratic equations, while factoring is a specific method that can be used to solve quadratic equations that can be factored easily.

Q: Can I use the quadratic formula to solve quadratic equations with complex solutions?

A: Yes, you can use the quadratic formula to solve quadratic equations with complex solutions. The quadratic formula will give you two solutions, one of which may be complex.

Q: How do I determine if a quadratic equation has real or complex solutions?

A: You can determine if a quadratic equation has real or complex solutions by looking at the discriminant, which is the expression under the square root in the quadratic formula. If the discriminant is positive, the equation has two real solutions. If the discriminant is zero, the equation has one real solution. If the discriminant is negative, the equation has two complex solutions.

Q: What is the discriminant?

A: The discriminant is the expression under the square root in the quadratic formula. It is given by:

$$b^2 - 4ac$$

Q: How do I use the discriminant to determine the nature of the solutions?

A: You can use the discriminant to determine the nature of the solutions by checking if it is positive, zero, or negative. If it is positive, the equation has two real solutions. If it is zero, the equation has one real solution. If it is negative, the equation has two complex solutions.

Conclusion

In this article, we have answered some of the most frequently asked questions about solving quadratic equations. We have covered topics such as the quadratic formula, factoring, and the discriminant. By understanding these concepts, you will be able to solve quadratic equations with ease.

Frequently Asked Questions

• What is a quadratic equation?
• How do I solve a quadratic equation?
• What is the quadratic formula?
• When should I use the quadratic formula?
• How do I use the quadratic formula?
• What is the difference between the quadratic formula and factoring?
• Can I use the quadratic formula to solve quadratic equations with complex solutions?
• How do I determine if a quadratic equation has real or complex solutions?
• What is the discriminant?
• How do I use the discriminant to determine the nature of the solutions?

Additional Resources

For more information on solving quadratic equations, readers can refer to the following resources:

• Khan Academy: Solving Quadratic Equations
• Mathway: Solving Quadratic Equations
• Wolfram Alpha: Solving Quadratic Equations

Final Answer

The final answer is: There is no final answer, as this article is a Q&A guide.