For the equation x^3 - 4x^2 + 5x - 2 = 0, which of the following is a root? (202

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Question: For the equation x^3 - 4x^2 + 5x - 2 = 0, which of the following is a root? (2023)

Options:

Correct Answer: 2

Exam Year: 2023

Solution:

By substituting x = 2 into the equation, we find that it satisfies the equation, thus x = 2 is a root.

For the equation x^3 - 4x^2 + 5x - 2 = 0, which of the following is a root? (2023)

For the equation x^3 - 4x^2 + 5x - 2 = 0, which of the following is a root? (2023)

Step 1: Identify the equation we need to solve: x^3 - 4x^2 + 5x - 2 = 0.
Step 2: Choose a value to test as a potential root. In this case, we will test x = 2.
Step 3: Substitute x = 2 into the equation: (2)^3 - 4(2)^2 + 5(2) - 2.
Step 4: Calculate (2)^3, which is 8.
Step 5: Calculate 4(2)^2, which is 4 * 4 = 16.
Step 6: Calculate 5(2), which is 10.
Step 7: Now substitute these values back into the equation: 8 - 16 + 10 - 2.
Step 8: Perform the calculations step-by-step: 8 - 16 = -8, then -8 + 10 = 2, and finally 2 - 2 = 0.
Step 9: Since the result is 0, this means that x = 2 satisfies the equation.
Step 10: 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.