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No. Complex zeros always come in conjugate pairs. So if a+bi is one zero, then a-bi is also a zero.
The fundamental theorem of algebra says
"Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers."
If you want to know how many complex root a given polynomial has, you might consider finding out how many real roots it has. This can be done with Descartes Rules of signs
- The maximum number of positive real roots can be found by counting the number of sign changes in f(x). The actual number of positive real roots may be the maximum, or the maximum decreased by a multiple of two.
- The maximum number of negative real roots can be found by counting the number of sign changes in f(-x). The actual number of negative real roots may be the maximum, or the maximum decreased by a multiple of two.
- Complex roots always come in pairs. That's why the number of positive or number of negative roots must decrease by two. Using the two rules for positive and negative signs along with the fact that complex roots come in pairs, you can determine the number of complex roots.
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Is it true that the degree of polynomial function determine the number of real roots?
Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)
Is it possible for a polynomial function of degree 3 to have no real zeros?
Yes - but only if the domain is restricted. Normally the domain is the whole of the real numbers and over that domain it must have at least one real zero.
What is the basic difference between algebraic expression and polynomial?
A polynomial is a type of algebraic expression. They differ in the number of terms that contain variables. An algebraic expression has at least 1 variable, while a polynomial has multiple terms with variables in it.
Does every rational function has at least one horizontal asymptote?
Nope not all the rational functions have a horizontal asymptote
What do you call a function whose graph is a non-vertical line?
It is a function. If the graph contains at least two points on the same vertical line, then it is not a function. This is called the vertical line test.
The polynomial given below has rootss?
You forgot to copy the polynomial. However, the Fundamental Theorem of Algebra states that every polynomial has at least one root, if complex roots are allowed. If a polynomial has only real coefficients, and it it of odd degree, it will also have at least one real solution.
What are the characteristics of a polynomial function?
Some of the characteristics of such a function are:The function is continuous (it doesn't make sudden jumps)The derivative is continuous (the function doesn't suddenly change its direction)The function is unbounded - as "x" grows larger and larger, f(x) approaches either plus or minus infinity (i.e., it grows without bounds).In the complex numbers, any polynomial has at least one zero.
Can a polynomial equation have no answer?
It depends on the domain. In the complex domain, a polynomial of order n must have n solutions, although some of these may be multiple solutions. In the real domain, a polynomial of odd order must have at least one real solution, while a polynomial of even order may have no real solutions.
What are the characteristics of a function?
Some of the characteristics of such a function are:The function is continuous (it doesn't make sudden jumps)The derivative is continuous (the function doesn't suddenly change its direction)The function is unbounded - as "x" grows larger and larger, f(x) approaches either plus or minus infinity (i.e., it grows without bounds).In the complex numbers, any polynomial has at least one zero.
If you are asked to write a polynomial function of least degree with real coefficients and with zeros of 2 and i square roots of seven what would be the degree of the polynomial also wright equation?
3y2-5xyz yay i figured it out!!!!
What are the characteristics of functionalism?
Some of the characteristics of such a function are:The function is continuous (it doesn't make sudden jumps)The derivative is continuous (the function doesn't suddenly change its direction)The function is unbounded - as "x" grows larger and larger, f(x) approaches either plus or minus infinity (i.e., it grows without bounds).In the complex numbers, any polynomial has at least one zero.
Who proved fundmental theorem of algebra?
The fundamental theorem of algebra was proved by Carl Friedrich Gauss in 1799. His proof demonstrated that every polynomial equation with complex coefficients has at least one complex root. This theorem laid the foundation for the study of complex analysis and was a significant contribution to mathematics.
Which function has no horizontal asymptote?
Many functions actually don't have these asymptotes. For example, every polynomial function of degree at least 1 has no horizontal asymptotes. Instead of leveling off, the y-values simply increase or decrease without bound as x heads further to the left or to the right.
Is it true that the degree of polynomial function determine the number of real roots?
Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)
How do you find out the number of imaginary zeros in a polynomial?
Descartes' rule of signs (see related link) can help you determine the maximum number of real roots. If the polynomial is odd powered, then there will be at least one real root. Any even powered polynomial can be factored into a bunch of quadratics [though they may not be rational or even pretty], and any odd-powered polynomial can be factored into a bunch of quadratics and one linear (this one would have the real root). So the quadratics may have pairs of real or complex roots (having an imaginary component).To clarify, when I say complex, I'm referring to the fact that there will be an imaginary component to the root, because actually the real numbers is a subset of the set of complex numbers.The order of the polynomial will tell you how many roots it will have. If you can graph the polynomial, then you can see if it crosses the x axis. If it is a 5th order polynomial, and crosses the x axis 3 times, then there are 3 real roots (the other two roots are complex).
What is the least degree a polynomial could have with an imaginary root with a multiplicity of three?
Since the question did not specify a rational polynomial, the answer is a polynomial of degree 3.
What is the coefficient of the term of degree 1 in the polynomial?
There's no way for me to tell until you show methe polynomial, or at least the term of degree 1 .
