If the polynomial equation x^3 - 6x^2 + 11x - 6 = 0 has roots a, b, and c, what

If the polynomial equation x^3 - 6x^2 + 11x - 6 = 0 has roots a, b, and c, what is the value of a + b + c? (2021)

If the polynomial equation x^3 - 6x^2 + 11x - 6 = 0 has roots a, b, and c, what is the value of a + b + c? (2021)

Step 1: Identify the polynomial equation given, which is x^3 - 6x^2 + 11x - 6 = 0.
Step 2: Recognize that this is a cubic polynomial, which means it has three roots, labeled as a, b, and c.
Step 3: Recall Vieta's formulas, which relate the coefficients of the polynomial to the sums and products of its roots.
Step 4: For a cubic polynomial of the form x^3 + px^2 + qx + r = 0, the sum of the roots (a + b + c) is equal to -p.
Step 5: In our polynomial, the coefficient of x^2 is -6. According to Vieta's, we take the opposite sign, which means we take 6.
Step 6: Therefore, the value of a + b + c is 6.

Vieta's Formulas – Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.
Polynomial Roots – Understanding how to find and interpret the roots of polynomial equations.