What is the maximum number of solutions a quartic function can have?
I assume you mean a polynomial of degree 4. In general, a polynomial of degree "n" can be separated into "n" linear factors. As a result, a polynomial of degree "n" has exactly "n" solutions - unless two or more of the factors are repeated; in which case the corresponding solution is said to be a multiple solution.
As an example:
(x - 2)(x - 5) = 0
has two solutions, namely 2 and 5; while
(x - 3)(x - 3)(x + 5) = 0
is of degree three, but has only two solutions, since the solution "3" is repeated.
An equation such as
x2 + 1 = 0
cannot be factored in the real numbers, so if you insist that the solutions be real, there are zero solutions. However, the polynomial can be factored in the complex numbers; in this case:
(x + i)(x - i) = 0,
resulting in the two complex solutions, -i and +i.
The similarities are that they are polynomial functions and therefore continuous and differentiable. A real cubic will has an odd number of roots (and so must have a solution), a quartic has an even number of roots and so may have no solutions.
The "maximum" function.
the maximum number of solutions to an euation is equal to the highest power expressed in the equation. 2x^2=whatever will have 2 answers
A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula. Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.
It really depends on which equation you're looking at
the maximum number of solutions to a quadratic equation is 2. However, usually there is only 1.
1331. The pattern is the quartic function: Un = (197n4 - 1854n3 + 6259n2 - 8730n + 4152)/24 for n = 1, 2, 3, ...
It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions. A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions. Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite. A function defined as follows: f(x) = 1 if x is real f(x) =… Read More
Linear programming is basically used to maximize profits (or some other function), when you have certain restrictions (for example, a limited amount of several resources).
No, this is not necessarily the case. A function can have an infinite range of solutions but not an infinite domain. This means that not every ordered pair would be a solution.
an infinite number of solutions
The area in the inequality gives you choices. Like the number of pounds that an elevator can carry is anything less than its maximum.
You can use the Max function and the Min function in a query to do it. They are both available when you use the Totals row in the query design grid.
In Calculus, to find the maximum and minimum value, you first take the derivative of the function then find the zeroes or the roots of it. Once you have the roots, you can just simply plug in the x value to the original function where y is the maximum or minimum value. To know if its a maximum or minimum value, simply do your number line to check. the x and y are now your… Read More
They are introduced to algebra through number machines. These are simple input-output processes. The pupils are given the machine's function, for example, "double the number and add 7". They are then given different inputs and asked to find the outputs. The next stage is giving them the inputs and outputs and asking them to work out the function. Finally, there are simple simultaneous equations - with integer solutions. They are introduced to algebra through number… Read More
The maximum number is 5.
The maximum number is 8.
the maximum is whatever the biggest number is and the range is the maximum (the largest number) minus the minimum (the smallest/lowest number)
It does not have any solutions! 14.8 is a number, not an equation, inequality or question and so has no solutions.
The following algorithm works for any number of integers: Assume the first number is the maximum - maximum = (first number). Compare your assumed maximum with the second number. If the second number is larger than the assumed maximum, replace the old assumed maximum with the second number. Repeat for the third number, for the fourth, etc. - always copying the nth. element to the assumed maximum if you find one that is larger than… Read More
the maximum is five.
Initially assume the maximum is equal to the first number. Then compare the maximum to the second number; if the second number is larger than the temporary maximum, assign the second number to the maximum. Repeat for the third number. If you use a for loop, and an array, you can easily expand the program to get the largest out of much larger sets of numbers. Initially assume the maximum is equal to the first… Read More
42, if you fit the quartic: 0.25*(x4 - 10x3 + 35x2 - 42x + 24)
There are 2 answers, +sqrt 7 and -sqrt7. Generally, the highest exponent in the expression (in this case 2) is the maximum number of possible answers.
Assume that the first number is the maximum (store it to a variable called, for example, "maximum"). Loop through the array; every time you find an array element (a number) that is larger than the previous maximum, replace variable "maximum" with this number.
The maximum number of US representatives to congress is 435.
The maximum number of electrons would be 2 No matter what the orbital is, the maximum number will always be 2
There is no maximum number for a an irregular concave polygon. If it must be convex, then there is a maximum of 3.
The phone number of the Museum Data Solutions is: 740-592-3399.
A number is not a function.
They have an infinite number of solutions.
There is no maximum.
There is no maximum, or minimum, number of monuments a city may have. They can have as many or few as the people wish. Therefore no city can have a maximum number
Yes; this is quite common for a quadratic equation. For example: x2 - 5x + 6 = 0 has the two solutions 2, and 3. A cubic equation may have up to 3 solutions; a polynomial of degree "n" can have up to "n" solutions. A trigonometric equation usually has an infinite number of solutions, because the sine function (for example) is periodic. Example: sin x = 0, with solutions 0, pi, 2 x pi… Read More
The answer will depend on where in the sequence the missing number is: Using only quartic polynomials, the solutions are: 3, 10, 25, 54, 103 10, 11.75, 25, 54, 103 10, 25, 33.8333..., 54, 103 10, 25, 54, 84.25, 103 10, 25, 54, 103, 178. Other functional forms will generate many more answers.
Using the quartic polynomial, (105x4 - 1038x3 + 3611x2 - 5118x + 2464)/8 the answer is 1703
Carbon is the element that forms maximum number of compounds
The maximum number of electrons in the s orbital is 2.
jupiter has the maximum number of satellites.... of almost 63 moons
The maximum number is 8 electrons in the second shell.
Maximum number of players on a cricket team is 11
8 maximum number
the maximum number is 560
There is no such thing as a solution for a single number!
A polygon is different than regular shapes, like square, triangle, rectangle. A polygon can be a regular shape like a square, but it can also have countless lines, angles, and shapes it it. Take a pencil and piece of paper. Start at the top, middle of the page. Draw a short line there. Now, start making "steps" down both sides from that line. Suddenly stop and draw a line toward the middle of the page… Read More
f(x) = 2 cos 3x The amplitude: A = |2| = 2 The maximum value of the function: 2 The minimum value of the function: -2 The range: [-2, 2]
Compare the maximum number of electrons possible in sublevel 3d with the maximum number that could be in sublevel 4d?
They are both capable of holding a maximum of 10
Base, or alkaline solutions.