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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 polynomial
Linear=Variable raised to the first power
Quadratic=Variable raised to the second power (or "squared")
Cubic=Variable raised to the third power (or "cubed")
Quartic=Variable raised to the fourth power
Quintic=Variable raised to the fifth power
Anything 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.
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Classification of polynomial according to the number of terms?
Strictly we do not classify polynomials by the number of terms but by the highest power of the variable (its degree).For example, if x is the variable then a polynomial with highest power...... x0 (degree 0) is a constant e.g. 4x0 = 4... x1 (degree 1) is linear e.g. 2x1 + 5 = 2x + 5... x2 (degree 2) is a quadratic e.g. 3x2 - 2x + 1... x3 (degree 3) is a cubic e.g. 2x3 - 3x2 - 2x + 1... x4 (degree 4) is a quartic e.g. 7x4 + 2x3 - 3x2 - 2x + 1(degree 5) quintic, (degree 6) sextic, (degree 7) septic, (degree 8) octic,...Although it appears as if the degree of a polynomial is always one less than the number of terms, in general this not the case. For example, x3 - 9 is cubic with only 2 terms or 4x8 is an octic with only one term.
What is a polynomial with four terms?
First off, it is NOT A QUINTIC! Typically a polynomial of four or more terms is called "a polynomial of n terms", where n is the number of terms. Only the one, two, and three term polynomials are referred to by a particular naming convention.
Determine the maximum or minimum value of y-3x2 12x-7 by completing the square?
Every polynomial defines a function, often called P. Linear and and quadratic function belong to a family of functions known as polynomial functions, which often are called P(x). When P(x) = 0, we call it an equation. Any value of x for which P(x) = 0 is a root of the equation and a zero of the function. Polynomials of the first few degrees have a special names such as:Degree 0: Constant functionDegree 1: Linear functionDegree 2: Quadratic functionDegree 3: Cubic functionDegree 4: Quartic functionDegree 5: Quintic functionSo, if we work a little bit to the given expression, we can turn it in a polynomial function of the second degree.y - 3x^2 = 12x - 7y - 3x^2 + 3x^2 = 12x - 7 + 3x^2y = 3x^2 + 12x - 7Let's write y = f(x) and f(x) = 3x^2 + 12x - 7, where a = 3, b = 12, and c = -7.Since a > 0, the parabola opens upward, so we have a minimum value of the function. The maximum or minimum value of the quadratic function occurs at x = -(b/2a).x = -12/6 = -2To find the minimum value of the function, which is also the y-value, we will find f(-2).f(-2) = 3(-2)^2 + 12(-2) - 7f(-2) = 12 - 24 - 7 = -19Thus the minimum value of the function is -19, and the vertex is (-2, -19)To find zeros, we solve f(x) = 0. So,f(x) = 3x^2 + 12x - 7f(x) = 03x^2 + 12x - 7 = 0 In order to solve this equation by completing the square, we need the constant term on the right hand side;3x^2 + 12x = 7 Add the square of one half of the coefficient of x to both sides, (6^2)3x^2 +12x + 36 = 7 + 36 Use the formula (a + b)^2 = a^2 + 2ab + b^2;(3x + 6)^2 = 43 Take the square root of both sides, and solve for x;3x + 6 = (+ & -)square root of 433x + 6 = (+ & -)(square root of 43) Subtract 6 to both sides;3x = (+ & -)(square root of 43) - 6 Divide both sides by 3;x = (square root of 43)/3 - 2 or x = -(square root of 43)/3 - 2The solution are (square root of 43) - 2 and -(square root of 43) - 2
What is this pattern rule for this pattern 21-66-42-61-84-56?
The numbers fit the quintic function: t(n) = (27n5 - 556n4 + 4253n3 - 14876n2 + 23440n - 11784)/24 for n = 1, 2, 3, etc
Is the polynomial 4x3 plus x plus 1 constant quintic cubic and quartic?
no
Scrabble words with the letter q in them?
quack, quaint, quarter, quick, quid, quip, quantify, quantum, quadratic, quartic, quintic, quicksilver, quicksand, que, quell,
Classify the polynomial.3r5 – 2r2 + 5r?
quintic
How do you name polynomials?
There are 2 ways to name a polynomial: by its degree (the highest power) and by the number of terms it has. Some of the most common names based on degree are: constant (meaning there is no variable--5 or 23, for instance; you could also realize that the variable is being raised to the 0 power), linear (the variable is raised to the first power--3x), quadratic (x2), cubic (x3), quartic (x4), and quintic (x5). Keep in mind that these terms could have any coefficients and any number of terms, just be sure you name it based on the highest power (ex: 3x4 + 5x3 - 2x is a quartic polynomial, whereas 3x4 + 5x3 - 2x5 would be a quintic polynomial). To name a polynomial based on the number of terms, make sure you've simplified it by combining all like terms, then count them up. If the polynomial has: 1 term--monomial (mono- means 1; like a monorail) 2 terms--binomial (bi- means 2; like a bicycle) 3 terms--trinomial (tri- means 3; like a triangle) 4 or more terms--just call it a polynomial, unless your teacher gives you more names (poly- means many; like a polygon). Keep in mind that these terms will often be used together: 3x4 + 5x3 - 2x is a quartic trinomial. (You may be thinking that I was wrong above where I called this same example a quartic polynomial--that was also correct, since monomial, binomial, and trinomial are all just more specific names for a polynomial)
Is it always true that the zeros of the derivative and the zeros of the polynomial always alternate in location along the horizontal axis?
A zero of the derivative will always appear between two zeroes of the polynomial. However, they do not always alternate. Sometimes two or more zeroes of the derivative will occur between two zeroes of a polynomial. This is often seen with quartic or quintic polynomials (polynomials with the highest exponent of 4th or 5th power).
Classification of polynomial according to the number of terms?
Strictly we do not classify polynomials by the number of terms but by the highest power of the variable (its degree).For example, if x is the variable then a polynomial with highest power...... x0 (degree 0) is a constant e.g. 4x0 = 4... x1 (degree 1) is linear e.g. 2x1 + 5 = 2x + 5... x2 (degree 2) is a quadratic e.g. 3x2 - 2x + 1... x3 (degree 3) is a cubic e.g. 2x3 - 3x2 - 2x + 1... x4 (degree 4) is a quartic e.g. 7x4 + 2x3 - 3x2 - 2x + 1(degree 5) quintic, (degree 6) sextic, (degree 7) septic, (degree 8) octic,...Although it appears as if the degree of a polynomial is always one less than the number of terms, in general this not the case. For example, x3 - 9 is cubic with only 2 terms or 4x8 is an octic with only one term.
Is x3-27 equals 0 a quadratic equation?
No, it's a cubic equation. A quadratic equation contains, as its term raised to the highest power, a square. Example: x2. A cubic equation contains, as its term raised to the highest power, a cube. Example: x3. A quartic equation contains, as its term raised to the highest power, a term raised to the fourth power. Example: x4. Quintic, x5. And so, on.
What was the discovery of neils abel?
Niels Henrik Abel proved that there is no general solution to the quintic equation (5th. degree polynomial) with radicals.
What is a average rate Average Rate?
if you are talking about linear rates-speed,.growth,interest,etc., then the average rate of the avarage rates is just that... the average. if ,you have 5 average rates, add them and divide by 5. if the average rates are quadradic,quartic,quintic and above- don't worry! its the same as above. if you're asking about an average of linear and quadratic or other,i"ll work on it(there is an answer) odelikeamo@gmail.com
What has the author Jerry Michael Shurman written?
Jerry Michael Shurman has written: 'Geometry of the quintic' -- subject(s): Curves, Quintic, Quintic Curves, Quintic equations
What is a polynomial with four terms?
First off, it is NOT A QUINTIC! Typically a polynomial of four or more terms is called "a polynomial of n terms", where n is the number of terms. Only the one, two, and three term polynomials are referred to by a particular naming convention.
How do you prove the quintic is not solvable?
You cannot prove it because it is not true. Some quintics ARE solvable. For example, if all the coefficients (in a quintic in x) sum to 0 then (x - 1) is a factor. So one solution is x = 1 and you are left qith a quartic. If the sum of odd coeffs equals the sum of even coeffs then (x + 1) is a factor. So, in some cases, at least, quintics are solvable.
