Struggling with Polynomial Functions: Can Complex Zeros Confuse You?

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In summary, the conversation is about someone seeking help with polynomial functions, specifically writing one with certain zeros and understanding how to factor polynomials. The conversation also mentions a test and studying for it.
  • #1
Sashman15
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hw help :( polynomial fxns.

Hey guys and gals, i'd appreciate if you could help me (well) with this question.

Write a polynomial function at minimum degree in standard form with real coefficients whose zeros include -1 and 1+4i

:O its hard for me, I am not a math person, and my precalculus teacher doesn't teach, he just talks.

Thanks!

btw i have a test tomorrow, so if you could tell me the answer and how you got it, that'd be awesome, because then i can study it and learn, thanks!
 
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  • #2
If a polynomial is factored to look like this:

(x-a)(x-b)=0

what does that mean?
 
  • #3
If a is a zero of a polynomial then x-a is a factor.

If a polynomial with real coefficients has 1+4i as a zero then it also has
1- 4i as a root.

If your polynomial has 1, 1+ 4i, and 1- 4i as zero what factors does it have? Multiply them together.
 

FAQ: Struggling with Polynomial Functions: Can Complex Zeros Confuse You?

What is a polynomial function?

A polynomial function is a mathematical function that is made up of terms consisting of constants, variables, and exponents, with the variables raised to non-negative integer powers. The general form of a polynomial function is f(x) = anxn + an-1xn-1 + ... + a1x + a0, where an, an-1, ..., a1, a0 are constants and n is a non-negative integer.

How do I graph a polynomial function?

To graph a polynomial function, you can start by finding the x-intercepts, or the points where the graph intersects the x-axis. These can be found by setting the function equal to 0 and solving for x. Then, you can find the y-intercept, or the point where the graph intersects the y-axis, by plugging in x = 0 to the function. You can also use the leading coefficient and degree of the polynomial to determine the end behavior of the graph. Finally, plot these points and any additional points you may need to find, and connect them with a smooth curve.

How do I find the roots of a polynomial function?

The roots of a polynomial function are the values of x that make the function equal to 0. To find the roots, you can use the quadratic formula for quadratic functions, or you can factor the function and set each factor equal to 0. For higher degree polynomials, you may need to use methods such as the rational root theorem or the Descartes' rule of signs to narrow down the possible roots before using other methods.

What is the degree of a polynomial function?

The degree of a polynomial function is the highest exponent of the variable in the function. For example, a polynomial function with the form f(x) = 5x3 + 2x2 + 3x + 1 has a degree of 3, since the highest exponent of x is 3. The degree of a polynomial can help determine the end behavior of the graph, as well as the number of roots it has.

How do I perform operations on polynomial functions?

To perform operations on polynomial functions, such as addition, subtraction, multiplication, and division, you can use the same methods as you would for regular numbers. For addition and subtraction, you can combine like terms by adding or subtracting the coefficients of terms with the same variable and exponent. For multiplication, you can use the distributive property to multiply each term in one function by each term in the other function. For division, you can use long division or synthetic division to find the quotient and remainder.

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