My Learning Cart
?
Categories
Account

For the cubic equation x^3 - 3x^2 + 3x - 1 = 0, which of the following is a root

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: For the cubic equation x^3 - 3x^2 + 3x - 1 = 0, which of the following is a root?

Options:

  1. -1
  2. 0
  3. 1
  4. 2

Correct Answer: 1

Solution: 

By substituting x = 1 into the equation, we find that it satisfies the equation, hence 1 is a root.

For the cubic equation x^3 - 3x^2 + 3x - 1 = 0, which of the following is a root

Practice Questions

Q1
For the cubic equation x^3 - 3x^2 + 3x - 1 = 0, which of the following is a root?
  1. -1
  2. 0
  3. 1
  4. 2

Questions & Step-by-Step Solutions

For the cubic equation x^3 - 3x^2 + 3x - 1 = 0, which of the following is a root?
  • Step 1: Write down the cubic equation: x^3 - 3x^2 + 3x - 1 = 0.
  • Step 2: Identify a potential root to test. In this case, we will test x = 1.
  • Step 3: Substitute x = 1 into the equation: (1)^3 - 3(1)^2 + 3(1) - 1.
  • Step 4: Calculate each term: (1)^3 = 1, -3(1)^2 = -3, 3(1) = 3, and -1 = -1.
  • Step 5: Combine the results: 1 - 3 + 3 - 1.
  • Step 6: Simplify the expression: 1 - 3 = -2, -2 + 3 = 1, and 1 - 1 = 0.
  • Step 7: Since the result is 0, this means that x = 1 satisfies the equation.
  • Step 8: Conclude that 1 is a root of the cubic equation.
  • Cubic Equations – Understanding the properties and solutions of cubic equations, including finding roots through substitution.
  • Substitution Method – Using substitution to test potential roots in polynomial equations.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks