# The Fundamental Theorem of Algebra

Total Word Count: 329
Send article as PDF
 Two roots of a third degree polynomial function f(x) are -4 and 4. Which statement describes the number and nature of all roots for this function? b. f(x) has three real roots. If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)? a. -9i According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots? fx = (3x^2 – 4x -5)(2x^6 – 5) If f(x) is a third degree polynomial function, how many distinct complex roots are possible? a. 0 or 2 According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 8x^7 – x^5 + x^3 + 6 c. 7 roots Patricia is studying a polynomial function f(x). Three given roots of f(x) are -11-√2i, 3 + 4i, and 10. Patricia concludes that f(x) must be a polynomial with degree 4. Which statement is true? d. Patricia is not correct because both 3 – 4i and -11+√2i must be roots. According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0 b. 3 roots Which of the following statements must be true about the polynomial function f(x)? b. If 1 + 13i is a root of f(x), then 1 – 13i is also a root of f(x). According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots? b. f(x) = (x + 2)^3 (x^2 – 7x + 3)^4 Which of the following describes the roots of the polynomial function f(x) = (x – 3)^4 (x + 6)^2? d. 3 with multiplicity 4 and -6 with multiplicity 2 According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 4x^5 – 3x d. 5 roots According to the Fundamental Theorem of Algebra, which polynomial function has exactly 6 roots? d. f(x) = 7x^6 + 3x^3 + 12 How many x intercepts appear on the graph of this polynomial function? f(x)= x^4 – x^3 + x^2 – x b. 2 x intercepts
Scroll to Top