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What do you know about the most possible number of zeros for a polynomial?
A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.
Are there only 3 degree's in a polynomial equation?
No. A polynomial can have as many degrees as you like.
What if the fourth derivative of a polynomial is zero?
There are many things that can be said about a polynomial function if its fourth derivative is zero, but the main thing you can know about this function from this information is that its order is 3 or less. Consider an nth order polynomial with only positive exponents: axn + bxn-1 + ... + cx2 + dx + e As you derive this function, its derivatives will eventually be equal to zero. The number of derivatives that are nonzero before they all become zero can tell you what order the polynomial function was. Consider an example, y = x4. y = x4 y' = 4x3 y'' = 12x2 y''' = 24x y(4) = 24 y(5) = 0 The original polynomial was of order 4, and its derivatives were nonzero up until its fifth derivative. From this, you can generalize to say that any function whose fifth derivative is equal to zero is of order 4 or less. If the function was of higher order than 4, its derivatives would not become zero until later. If the function was of lower order than 4, its fifth derivative would still be zero, but it would not be the first zero-valued derivative. So this experimentation yielded a rule that the first zero-valued derivative is one greater than the order of the polynomial. Your problem states that some polynomial has a fourth derivative that is zero. Our working rule states that this polynomial can be of highest order 3. So, your polynomial can be, at most, of the form: y = ax3 + bx2 + cx + d Letting the constants a through d be any real number (including zero), this general form expresses any polynomial that will satisfy your condition.
How many terms are in the polynomial?
4
How many terms does the polynomial have?
As many as you like. A polynomial in 1 variable, and of degree n, can have n+1 terms where n is any positive integer.
how many roots does the graphed polynomial function have?
here is the graph
How many unique roots will a third degree polynomial function have?
It can have 1, 2 or 3 unique roots.
At most how many unique roots will a fourth-degree polynomial have?
According to the rational root theorem, which of the following are possible roots of the polynomial function below?F(x) = 8x3 - 3x2 + 5x+ 15
How many real roots will a 3rd degree polynomial have?
A third degree polynomial could have one or three real roots.
At most how many unique roots will a fourth degree polynomial have?
4, the same as the degree of the polynomial.
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.)
At most how many unique roots will a third-degree polynomial have?
A third-degree equation has, at most, three roots. A fourth-degree polynomial has, at most, four roots. APEX 2021
How many x-intercepts does a quartic polynomial function having 4 distinct real roots have?
Each distinct real root is an x-intercept. So the answer is 4.
The polynomial 32 plus 4x plus 3 has how many roots?
1
At most, how many unique roots will a fourth-degree polynomial have?
Four.Four.Four.Four.
At most how many unique roots will a fifth-degree polynomial have?
5, Using complex numbers you will always get 5 roots.
How many times does a porabola cross the x-axis when using imaginary numbers?
NONE If both roots are imaginary, the means the parabola does NOT cross the x-axis at all. The place where a function crosses the x- axis has the coordinate (x,0) for some value of x. That means if you plug in x to the function or polynomial, you get 0. This is equivalent to saying that x is a root of the polynomial. But if the only roots are imaginary, there will be no point (x,0) for any real number x.
