Suggested languages for you:

Americas

Europe

Problem 627

# Find all solutions of the equation $\mathrm{x}^{3}-3 \mathrm{x}^{2}-10 \mathrm{x}=0$

Expert verified
The solutions for the equation $$x^3 - 3x^2 -10x = 0$$ are $$x = 0$$, $$x = 5$$, and $$x = -2$$.
See the step by step solution

## Step 1: Factor out the common term

We can factor out the common term (x) from the given equation. This gives us: $x(x^2 - 3x - 10) = 0$

## Step 2: Factor the quadratic equation

Now, we need to factor the quadratic equation $$x^2 - 3x - 10$$. To do that, we find two numbers whose product is equal to the constant term (-10) and whose sum is equal to the coefficient of the x term (-3). We find that these two numbers are -5 and 2. So, we can write the quadratic equation as: $(x - 5)(x + 2) = 0$ Now, our factored equation looks like this: $x(x - 5)(x + 2) = 0$

## Step 3: Find the solutions (roots)

The solutions (roots) of the equation are the values of x that make the equation equal to zero. Based on the factored form, we can see that there are three possible solutions: 1. $$x = 0$$: The equation is equal to zero when x is 0. 2. $$x - 5 = 0$$: The equation is equal to zero when x is 5. 3. $$x + 2 = 0$$: The equation is equal to zero when x is -2. Therefore, the solutions for the equation $$x^3 - 3x^2 -10x = 0$$ are $$x = 0$$, $$x = 5$$, and $$x = -2$$.

We value your feedback to improve our textbook solutions.

## Access millions of textbook solutions in one place

• Access over 3 million high quality textbook solutions
• Access our popular flashcard, quiz, mock-exam and notes features

## Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

• Flashcards & Quizzes
• AI Study Assistant
• Smart Note-Taking
• Mock-Exams
• Study Planner