For the polynomial x^3 - 3x^2 + 3x - 1, what is the value of the sum of the root

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Question: For the polynomial x^3 - 3x^2 + 3x - 1, what is the value of the sum of the roots? (2019)

Options:

Correct Answer: 3

Exam Year: 2019

Solution:

The sum of the roots is given by -b/a = 3/1 = 3.

For the polynomial x^3 - 3x^2 + 3x - 1, what is the value of the sum of the roots? (2019)

For the polynomial x^3 - 3x^2 + 3x - 1, what is the value of the sum of the roots? (2019)

Step 1: Identify the polynomial given in the question, which is x^3 - 3x^2 + 3x - 1.
Step 2: Recognize that the polynomial is in the standard form ax^3 + bx^2 + cx + d, where a, b, c, and d are coefficients.
Step 3: From the polynomial, identify the coefficients: a = 1 (for x^3), b = -3 (for x^2), c = 3 (for x), and d = -1 (constant term).
Step 4: Use the formula for the sum of the roots of a polynomial, which is -b/a.
Step 5: Substitute the values of b and a into the formula: -(-3)/1.
Step 6: Simplify the expression: 3/1 = 3.
Step 7: Conclude that the sum of the roots of the polynomial is 3.

Vieta's Formulas – Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.