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What is the quartic polynomial function with rational coefficients that has roots you and 2i?
Wiki User
∙ 12y ago
(x - u)*(x - u)*(x + 2i)*(x - 2i)
= (x2 - 2xu + u2)*(x2 + 4)
= x4 - 2x3u + x2(u2 + 4) - 8xu + 4u2
Wiki User
∙ 12y ago
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What does polynomial with rational coefficients mean?
Let's define this question one word at a time. A polynomial is an equation with the variable x raised to whole number powers other than 0. This may include 2x + 3, or x2 - 8x + 16, or even x5 - 4x3 + 9. Coefficients are the numbers multiplied by the x term in question. The term 6x3 has a coefficient of 6, the term -x/2 has a coefficient of -1/2 and the term x2 has a coefficient of 1. Rational numbers are those which can be written as a ratio, or a fraction. This means its decimal notation will either have a finite amount of digits, like 0.625 (5/8), or a repeating series of decimals, e.g. 2.16666... or 13/6. Rational numbers can only be formed with addition, subtraction, multiplication and division - this means it excludes functions like taking the square root, the sine, or the log of a number. In summary, a polynomial with rational coefficients is an expression with multiple terms, such as ax2 + bx + c, where the coefficients 'a' and 'b' (and typically 'c' as well, as it is the coefficient of x0 which is 1 by definition, and is therefore being multiplied by 1) are rational numbers. This can extend to mean a polynomial of any degree, be it linear (x), cubic (x3), quartic (x4) or anything higher - so long as the coefficients of all the x terms are rational.
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.
What is a depressed polynomial?
It is nothing more than a polynomial that is equivalent to another, but has fewer terms. For an example, see Wikipedia, under "quartic equation".
What are quadratic polynomial quartic polynomial constant polynomial and quintic polynomial?
Those words refer to the degree, or highest exponent that modifies a variable, or the polynomial.Constant=No variables in the polynomialLinear=Variable raised to the first powerQuadratic=Variable raised to the second power (or "squared")Cubic=Variable raised to the third power (or "cubed")Quartic=Variable raised to the fourth powerQuintic=Variable raised to the fifth powerAnything higher than that is known as a "6th-degree" polynomial, or "21st-degree" polynomial. It all depends on the highest exponent in the polynomial. Remember, exponents modifying a constant (normal number) do not count.
What is quartic and biquadratic?
A quartic is a polynomial of degree 4, meaning the highest exponent is 4. Biquadratic can mean the same thing, but most mathematicians use the term biquadratic to refer to an equation of degree 4 with no odd powers. So for example we cannot have an x3 term. An example of a biquadratic is: x4 +x2 + 22=0
Can you use the quadratic formula after reducing a polynomial to a quartic function?
No.
Once you have reduced a polynomial to a quartic function you can always use the quadratic formula to finish the problem?
false
What is another name for a 4th degree polynomial?
A fourth degree polynomial can be called a "quartic".
What does polynomial with rational coefficients mean?
Let's define this question one word at a time. A polynomial is an equation with the variable x raised to whole number powers other than 0. This may include 2x + 3, or x2 - 8x + 16, or even x5 - 4x3 + 9. Coefficients are the numbers multiplied by the x term in question. The term 6x3 has a coefficient of 6, the term -x/2 has a coefficient of -1/2 and the term x2 has a coefficient of 1. Rational numbers are those which can be written as a ratio, or a fraction. This means its decimal notation will either have a finite amount of digits, like 0.625 (5/8), or a repeating series of decimals, e.g. 2.16666... or 13/6. Rational numbers can only be formed with addition, subtraction, multiplication and division - this means it excludes functions like taking the square root, the sine, or the log of a number. In summary, a polynomial with rational coefficients is an expression with multiple terms, such as ax2 + bx + c, where the coefficients 'a' and 'b' (and typically 'c' as well, as it is the coefficient of x0 which is 1 by definition, and is therefore being multiplied by 1) are rational numbers. This can extend to mean a polynomial of any degree, be it linear (x), cubic (x3), quartic (x4) or anything higher - so long as the coefficients of all the x terms are rational.
What kind of polynomial is shown 0.2x4 - 5x2 - 7x?
I am assuming this is: .2x4 - 5x2 - 7x, which would be a Quartic Polynomial.
What is a quartic?
A quartic is an algebraic equation or function of the fourth degree.
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.
Is the polynomial 4x3 plus x plus 1 constant quintic cubic and quartic?
no
What is a depressed polynomial?
It is nothing more than a polynomial that is equivalent to another, but has fewer terms. For an example, see Wikipedia, under "quartic equation".
What kind of sequence is the pattern 1 6 7 13 20?
There are many possible answers. But given 5 points, an answer that can be guaranteed is that it is a polynomial of degree 4 (a quartic).In this case, Un = (-13n4 + 166n3 - 719n2 + 1310n - 720)/24There are many possible answers. But given 5 points, an answer that can be guaranteed is that it is a polynomial of degree 4 (a quartic).In this case, Un = (-13n4 + 166n3 - 719n2 + 1310n - 720)/24There are many possible answers. But given 5 points, an answer that can be guaranteed is that it is a polynomial of degree 4 (a quartic).In this case, Un = (-13n4 + 166n3 - 719n2 + 1310n - 720)/24There are many possible answers. But given 5 points, an answer that can be guaranteed is that it is a polynomial of degree 4 (a quartic).In this case, Un = (-13n4 + 166n3 - 719n2 + 1310n - 720)/24
What are quadratic polynomial quartic polynomial constant polynomial and quintic polynomial?
Those words refer to the degree, or highest exponent that modifies a variable, or the polynomial.Constant=No variables in the polynomialLinear=Variable raised to the first powerQuadratic=Variable raised to the second power (or "squared")Cubic=Variable raised to the third power (or "cubed")Quartic=Variable raised to the fourth powerQuintic=Variable raised to the fifth powerAnything higher than that is known as a "6th-degree" polynomial, or "21st-degree" polynomial. It all depends on the highest exponent in the polynomial. Remember, exponents modifying a constant (normal number) do not count.
What has the author Leonarda Burke written?
Leonarda Burke has written: 'On a case of the triangles in-and-circumscribed to a rational quartic curve with a line of symmetry' -- subject(s): Quartic Curves, Triangle
