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anonymous
 4 years ago
According to The Fundamental Theorem of Algebra, how many zeros does the function f(x) = 15x^17 + 41x^12 + 13x^3 – 10 have ?
Answer:
A)3
B)12
C)32
D)17
Please help meeee:)
anonymous
 4 years ago
According to The Fundamental Theorem of Algebra, how many zeros does the function f(x) = 15x^17 + 41x^12 + 13x^3 – 10 have ? Answer: A)3 B)12 C)32 D)17 Please help meeee:)

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JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1What is the statement of the Fund Theorem of Algebra?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1The fundamental theorem of algebra states that every nonconstant singlevariable polynomial with complex coefficients has at least one complex root. Equivalently, the field of complex numbers is algebraically closed. Sometimes, this theorem is stated as: every nonzero singlevariable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted up to its multiplicity. Although this at first appears to be a stronger statement, it is a direct consequence of the other form of the theorem, through the use of successive polynomial division by linear factors.

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1That's a fancy way of saying a firstorder polynomial has 1 root a secondorder polynomial has 2 roots a thirdorder polynomial has 3 roots etc. Given all that then, what order is your polynomial and how many roots must it have?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1f(x) = 15x^17 + 41x^12 + 13x^3 – 10 The order of a polynomial in one variable x is the highest power of x in the polynomial. For instance x  2 is first order, because the highest power of x is x^1 = x x^2  x  2 is second order, because the highest power of x is x^2 15x^3 + 15x  27 is third order, because the highest power of x is x^3 Hence given your polynomial 15x^17 + 41x^12 + 13x^3 – 10 what is its order?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1What's the higher power of x in f(x) = 15x^17 + 41x^12 + 13x^3 – 10 There are three choices: x^17 x^12 x^3

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1Right. The highest power of x is x^17 ...

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1hence f(x) is a 17thorder polynomial ...

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.1hence by the Fundamental Theorem of Algebra f(x) = 15x^17 + 41x^12 + 13x^3 – 10 has 17 roots
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