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What else can I help you with?
Is it possible that the polynomial function doesn't have zeros?
In the real domain, yes. In the complex domain, no.
Can you have quadratic function with one real root and are complex root?
Yes, but in this case, the coefficients of the polynomial can not all be real.
What is the difference between a power functions and a polynomial functions?
A power function is of the form xa where a is a real number. A polynomial function is of the form anxn + an-1xn-1 + ... + a1x + a0 for some positive integer n, and all the ai are real constants.
Can a polynomial be no rational zeros but have real zeros?
Yes, a polynomial can have no rational zeros while still having real zeros. This occurs, for example, in the case of a polynomial like (x^2 - 2), which has real zeros ((\sqrt{2}) and (-\sqrt{2})) but no rational zeros. According to the Rational Root Theorem, any rational root must be a factor of the constant term, and if none exist among the possible candidates, the polynomial can still have irrational real roots.
What does it mean to be a root of a polynomial?
A root of a polynomial is a value of the variable for which the polynomial evaluates to zero. In other words, if ( p(x) ) is a polynomial, then a number ( r ) is a root if ( p(r) = 0 ). Roots can be real or complex and are critical for understanding the behavior and graph of the polynomial function. The Fundamental Theorem of Algebra states that a polynomial of degree ( n ) has exactly ( n ) roots, counting multiplicities.
What are some real life Applications of Polynomial Functions?
That depends on what you mean with "real-life". You won't need polynomial functions to sell stuff at a supermarket, or to cut off a dead branch from your tree... but if you work in science and engineering, you will need some really advanced math - much more than a simple polynomial function.
Is it possible that the polynomial function doesn't have zeros?
In the real domain, yes. In the complex domain, no.
Can you have quadratic function with one real root and are complex root?
Yes, but in this case, the coefficients of the polynomial can not all be real.
What is the difference between a power functions and a polynomial functions?
A power function is of the form xa where a is a real number. A polynomial function is of the form anxn + an-1xn-1 + ... + a1x + a0 for some positive integer n, and all the ai are real constants.
Do vampires exist in real life today?
No, In real life days vampired no not exist
Does Nods limbs exist in real life?
nods limbs doesn't exist in real life!!
What are some examples in real life in which you might use polynomial division?
niga
Does Sonadow exist in real life?
No, all Sonic characters are fictional, and don't exist in real life.
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.)
What is a movie gun?
Either one made to function with blanks only or something made up that doesn't exist in real life.
Can a polynomial be no rational zeros but have real zeros?
Yes, a polynomial can have no rational zeros while still having real zeros. This occurs, for example, in the case of a polynomial like (x^2 - 2), which has real zeros ((\sqrt{2}) and (-\sqrt{2})) but no rational zeros. According to the Rational Root Theorem, any rational root must be a factor of the constant term, and if none exist among the possible candidates, the polynomial can still have irrational real roots.
Why does every polynomial have a real root?
1+x2 is a polynomial and doesn't have a real root.
