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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.)
What else can I help you with?
What is a zero degree polynomial called?
a polynomial of degree...............is called a cubic polynomial
What is the leading coefficient in a polynomial?
It is the number (coefficient) that belongs to the variable of the highest degree in a polynomial.
What is the difference between a transcendental an algebraic function?
An algebraic function is a function built from polynomial and combined with +,*,-,/ signs. The transcendental it is not built from polynomial like X the power of Pie plus 1. this function is transcendental because the power pi is not integer number in result it can't be a polynomial.
What is the minimum number of x-intercepts that a 7th degree polynomial might have?
1
How do you find the degree of polynomials?
First look at the degree of each term: this is the power of the variable. The highest such number, from all the terms in the polynomial is the degree of the polynomial. Thus x2 + 1/7*x + 3 has degree 2. x + 7 - 2x3 + 0.8x5 has degree 5.
What is a zero degree polynomial called?
a polynomial of degree...............is called a cubic polynomial
Is the number of y-intercepts for a polynomial determined by the degree of the polynomial?
no...
Can a polynomial have more zeros than the highest degree of the function?
no a plynomial can not have more zeros than the highest (degree) number of the function at leas that is what i was taught. double check the math.
Is 13 a polynomial If it is find its degree and classify it by the number of its terms?
13 is not a polynomial.
What is the relationship between the degree of a polynomial and the number of roots it has?
In answering this question it is important that the roots are counted along with their multiplicity. Thus a double root is counted as two roots, and so on. The degree of a polynomial is exactly the same as the number of roots that it has in the complex field. If the polynomial has real coefficients, then a polynomial with an odd degree has an odd number of roots up to the degree, while a polynomial of even degree has an even number of roots up to the degree. The difference between the degree and the number of roots is the number of complex roots which come as complex conjugate pairs.
What is the leading coefficient in a polynomial?
It is the number (coefficient) that belongs to the variable of the highest degree in a polynomial.
How many roots will a fifth-degree polynomial function have?
A fifth-degree polynomial function will have exactly five roots, counting multiplicities. This means that some of the roots may be repeated or complex, but the total number of roots, including these repetitions, will always equal five. If the polynomial has real coefficients, some of the roots may also be non-real complex numbers, which occur in conjugate pairs.
Is the highest degree of any of the terms in the polynomial?
Yes, in a polynomial, the highest degree is determined by the term with the greatest exponent on its variable. For example, in the polynomial (3x^4 + 2x^2 - 5), the highest degree is 4, which comes from the term (3x^4). The degree of a polynomial is significant as it influences the polynomial's behavior and the number of roots it can have.
What is The largest exponent which is shown in a polynomial is?
The largest exponent in a polynomial is referred to as its degree. The degree of a polynomial indicates the highest power of the variable present in the expression. For example, in the polynomial (3x^4 + 2x^3 - x + 7), the degree is 4, corresponding to the term (3x^4). The degree plays a crucial role in determining the polynomial's behavior and the number of possible roots.
What is the LARGEST number of real zeros a polynomial with degree n can have?
A polynomial of degree ( n ) can have at most ( n ) real zeros. This is a consequence of the Fundamental Theorem of Algebra, which states that a polynomial of degree ( n ) has exactly ( n ) roots in the complex number system, counting multiplicities. Therefore, while all roots can be real, the maximum number of distinct real zeros a polynomial can possess is ( n ).
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 is the classification of terms according to number and degree?
the degree of polynomial is determined by the highest exponent its variable has.
