For the equation x^3 - 6x^2 + 11x - 6 = 0, which of the following is a root?

₹0.0

Question: For the equation x^3 - 6x^2 + 11x - 6 = 0, which of the following is a root?

Options:

Correct Answer: 2

Solution:

By substituting x = 2 into the equation, we find that 2 is a root since 2^3 - 6(2^2) + 11(2) - 6 = 0.

For the equation x^3 - 6x^2 + 11x - 6 = 0, which of the following is a root?

For the equation x^3 - 6x^2 + 11x - 6 = 0, which of the following is a root?

Step 1: Identify the equation we need to solve: x^3 - 6x^2 + 11x - 6 = 0.
Step 2: We want to check if x = 2 is a root of the equation.
Step 3: Substitute x = 2 into the equation: 2^3 - 6(2^2) + 11(2) - 6.
Step 4: Calculate 2^3, which is 8.
Step 5: Calculate 6(2^2), which is 6 * 4 = 24.
Step 6: Calculate 11(2), which is 22.
Step 7: Now, put all the values into the equation: 8 - 24 + 22 - 6.
Step 8: Simplify the expression: 8 - 24 = -16, then -16 + 22 = 6, and finally 6 - 6 = 0.
Step 9: Since the result is 0, we conclude that x = 2 is a root of the equation.

Polynomial Roots – Understanding how to find roots of polynomial equations by substitution.
Substitution Method – Using substitution to verify if a given value is a root of the polynomial.