Solve For { P $} . . . { (3p - 5)(p - 2) = 0\$}

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. One of the most common methods of solving equations is by using the zero product property, which states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero. In this article, we will use this property to solve the equation {(3p - 5)(p - 2) = 0$}$ and find the value of { p $}$.

Understanding the Zero Product Property

The zero product property is a fundamental concept in algebra that helps us solve equations by finding the value of unknown variables. It states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero. This means that if we have an equation of the form {(a)(b) = 0$}$, then either {a = 0$}$ or {b = 0$}$.

Applying the Zero Product Property to the Given Equation

Now that we have understood the zero product property, let's apply it to the given equation {(3p - 5)(p - 2) = 0$}$. According to the zero product property, if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero. In this case, we have two factors: {(3p - 5)$] and [(p−2)$].Therefore,either\[(p - 2)\$]. Therefore, either \[(3p - 5) = 0$}$ or {(p - 2) = 0$}$.

Solving the First Factor

Let's start by solving the first factor: {(3p - 5) = 0$}$. To solve this equation, we need to isolate the variable {p$. We can do this by adding [5\$} to both sides of the equation, which gives us ${$3p = 5$. Then, we can divide both sides of the equation by [3$,whichgivesus\[3\$, which gives us \[p = \frac{5}{3}$.

Solving the Second Factor

Now, let's solve the second factor: [(p−2)=0$.Tosolvethisequation,weneedtoisolatethevariable\[(p - 2) = 0\$. To solve this equation, we need to isolate the variable \[p$. We can do this by adding [2\$} to both sides of the equation, which gives us {p = 2$. This is the value of [p\$} that satisfies the second factor.

Conclusion

In this article, we used the zero product property to solve the equation {(3p - 5)(p - 2) = 0$. We found that either [(3p - 5) = 0\$} or {(p - 2) = 0$. We then solved each factor separately and found that [p=53$and\[p = \frac{5}{3}\$ and \[p = 2$. These are the two possible values of [p\$} that satisfy the given equation.

Final Answer

The final answer is {p = \frac{5}{3}$ or [$p = 2$.

Introduction

In our previous article, we used the zero product property to solve the equation {(3p - 5)(p - 2) = 0$. We found that either [(3p - 5) = 0\$} or {(p - 2) = 0$. We then solved each factor separately and found that [p=53$and\[p = \frac{5}{3}\$ and \[p = 2$. In this article, we will answer some frequently asked questions related to the solution of the equation.

Q&A

Q: What is the zero product property?

A: The zero product property is a fundamental concept in algebra that helps us solve equations by finding the value of unknown variables. It states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Q: How do we apply the zero product property to the given equation?

A: To apply the zero product property to the given equation, we need to identify the factors and then set each factor equal to zero. In this case, we have two factors: [(3p−5)$]and\[(3p - 5)\$] and \[(p - 2)$. Therefore, either [(3p - 5) = 0\$} or {(p - 2) = 0$}$.

Q: How do we solve the first factor?

A: To solve the first factor, {(3p - 5) = 0$, we need to isolate the variable [$p$. We can do this by adding [5\$} to both sides of the equation, which gives us ${$3p = 5$. Then, we can divide both sides of the equation by [3$,whichgivesus\[3\$, which gives us \[p = \frac{5}{3}$.

Q: How do we solve the second factor?

A: To solve the second factor, [(p−2)=0$,weneedtoisolatethevariable\[(p - 2) = 0\$, we need to isolate the variable \[p$. We can do this by adding [2\$} to both sides of the equation, which gives us {p = 2$. This is the value of [p\$} that satisfies the second factor.

Q: What are the possible values of {p$}$ that satisfy the given equation?

A: The possible values of {p$}$ that satisfy the given equation are {p = \frac{5}{3}$ and [p=2$.Thesearethetwopossiblevaluesof\[p = 2\$. These are the two possible values of \[p$}$ that satisfy the given equation.

Q: Can we have more than one solution to the equation?

A: Yes, we can have more than one solution to the equation. In this case, we have two possible values of {p$}$ that satisfy the given equation.

Q: How do we check the solutions?

A: To check the solutions, we need to plug each solution back into the original equation and see if it is true. In this case, we can plug {p = \frac{5}{3}$ and [$p = 2$ back into the original equation and see if it is true.

Conclusion

In this article, we answered some frequently asked questions related to the solution of the equation [(3p−5)(p−2)=0$.Wefoundthateither\[(3p - 5)(p - 2) = 0\$. We found that either \[(3p - 5) = 0$}$ or {(p - 2) = 0$. We then solved each factor separately and found that [p=53$and\[p = \frac{5}{3}\$ and \[p = 2$. These are the two possible values of [p\$} that satisfy the given equation.

Final Answer

The final answer is [p=53$or\[p = \frac{5}{3}\$ or \[p = 2$.