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How do you write polynomial of least degree with roots 6 and -5?
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Degree of a terms of polynomial?
The degree of a polynomial is the highest degree of its terms. The degree of a term is the sum of the exponents of the variables that appear in it.For example, the polynomial 8x2y3 + 5x - 10 has three terms. The first term has a degree of 5, the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial is degree five.
What is a second degree polynomial function?
A second-degree polynomial function is a function of the form: P(x) = ax2 + bx + cWhere a ≠ 0.
What is a polynomial equation of least degree for roots 3 and -5 and 1?
(x - 3)*(x + 5)*(x - 1) = 0 (x2 - 3x + 5x - 15)*(x - 1) = 0 (x2 + 2x - 15)*(x - 1) = 0 (x3 + 2x2 - 15x - x2 - 2x + 15) = 0 ie x3 + x2 - 17x + 15 = 0
What are the values at which the graph of a polynomial crosses the x-axis?
The graph of a polynomial in X crosses the X-axis at x-intercepts known as the roots of the polynomial, the values of x that solve the equation.(polynomial in X) = 0 or otherwise y=0
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 write polynomial of least degree with roots 6 and -5?
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What is the polynomial of degree 0?
A polynomial of degree 0 is a polynomial without any variables, such as 9.
What are the roots of polynomial?
The "roots" of a polynomial are the solutions of the equation polynomial = 0. That is, any value which you can replace for "x", to make the polynomial equal to zero.
What is the degree of a constant polynomial?
a constant polynomial has a degree zero (0).
How many real roots can a fourth degree polynomial have?
Upto 4. If the coefficients are all real, then it can have only 0, 2 or 4 real roots.
How can a rational equation have more than one solution?
A rational equation can be multiplied by the least common multiple of its denominators to make it into a polynomial equation. The degree of this polynomial is the highest power (of the variable) that appears in it. It can be proven that a polynomial of degree n must have n roots in the complex domain. However, there may be fewer roots in the real domain. This is because if the coefficients are real then there may be pairs of complex roots [conjugates] which will not count as real roots. Also, there may be identical roots of multiple order. For example, x4 - 1 = 0 has 4 complex roots. These are 1, -1, i and -i where i is the imaginary root of -1. There are only 2 real roots -1 and +1. x4 = 0 has 4 multiple roots, each of which is 0. Thus x = 0 is a root of multiplicity 4.
How can you quickly determine the number of roots a polynomial will have by looking at the equation?
In the complex field, a polynomial of degree n (the highest power of the variable) has n roots. Some of these roots may be multiple roots. However, if the domain is the real numbers (or a subset) then there is no easy way. The degree only gives the maximum number of roots - there may be no real root. For example x2 + 1 = 0.
How is the degree of a simplified polynomial found?
The degree of a polynomial is equal to the highest degree of its terms. In the case that there is no exponent, the degree is 1. If there is no variable, the degree is 0.
Is a polynomial of degree 0 is a constant term?
Yes, a polynomial of degree 0 is a constant term. In mathematical terms, a polynomial is defined as a sum of terms consisting of a variable raised to a non-negative integer power multiplied by coefficients. Since a degree 0 polynomial has no variable component, it is simply a constant value.
What is the smallest degree a polynomial can have?
The smallest is 0: the polynomial p(x) = 3, for example.
Is 21 a polynomial?
Not in the normal sense but it could be considered a degenerate polynomial of degree 0.
