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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.
What else can I help you with?
What function is used to determine highest number in a range?
The "maximum" function.
How do you determine the number of solutions of an equation?
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
How do you find maximum number of solutions algebra?
It really depends on which equation you're looking at
What is the maximum number of relative extreme contained in the graph of this function xxx plus X?
To find the maximum number of relative extrema of the function ( f(x) = x^3 + x ), we first compute its derivative: ( f'(x) = 3x^2 + 1 ). Since ( f'(x) ) is always positive (as ( 3x^2 + 1 > 0 ) for all ( x )), the function is strictly increasing and does not have any relative extrema. Therefore, the maximum number of relative extrema contained in the graph of this function is zero.
Explain how the number of solutions for a quadratic equation relates to the graph of the function?
The number of solutions for a quadratic equation corresponds to the points where the graph of the quadratic function intersects the x-axis. If the graph touches the x-axis at one point, the equation has one solution (a double root). If it intersects at two points, there are two distinct solutions, while if the graph does not touch or cross the x-axis, the equation has no real solutions. This relationship is often analyzed using the discriminant from the quadratic formula: if the discriminant is positive, there are two solutions; if zero, one solution; and if negative, no real solutions.
What are some similarities and differences between quartic and cubic functions?
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.
What function is used to determine highest number in a range?
The "maximum" function.
How many Number of basic solutions optimisation problem?
The number of basic solutions in an optimization problem is determined by the number of decision variables. For a problem with n decision variables, there can be a maximum of n basic solutions.
How do you determine the number of solutions of an equation?
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
How do you find maximum number of solutions algebra?
It really depends on which equation you're looking at
Why does the discriminant determine the number and type of the solutions for a quadratic equation?
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.
In general how many distinct solutions are there to a quadratic equation?
the maximum number of solutions to a quadratic equation is 2. However, usually there is only 1.
What is the next number in the series 1 2 8 48 348?
1331. The pattern is the quartic function: Un = (197n4 - 1854n3 + 6259n2 - 8730n + 4152)/24 for n = 1, 2, 3, ...
What function compare the numbers in the specified range and then return with the largest number?
Maximum.
What is the maximum number of times the graph of the quadratic function can cross the x-axis?
Two.
How do you recognize when an equation has no real solution or an infinite number of solutions?
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) = 0 if x is not real has no real solutions but an infinite number of solutions in complex numbers.
What is the time complexity of finding the maximum element in a list using the Python max function?
The time complexity of finding the maximum element in a list using the Python max function is O(n), where n is the number of elements in the list.
