What is the solution set of x 4 9 x – What is the solution set of x^4 – 9x? Embark on an enlightening journey as we delve into the intricacies of this equation, uncovering its solution set and exploring its multifaceted nature. From factorization to graphical representations, prepare to unravel the secrets of this mathematical enigma.
In this comprehensive analysis, we will meticulously define the concept of a solution set, meticulously solve the equation x^4 – 9x, and unveil the characteristics of its solution set. We will then embark on a visual adventure, creating a graphical representation to illustrate the values of x that satisfy the equation.
Solution Set of x^4
9x
9x
In mathematics, the solution set of an equation is the set of all values that satisfy the equation. For example, the solution set of the equation x + 2 = 5 is the set 3, because 3 is the only value that makes the equation true.
Solving the Equation x^4
9x
9x
To find the solution set of the equation x^4 – 9x, we can factor the equation as follows:
x^4 – 9x = x(x^3 – 9) = x(x – 3)(x^2 + 3x + 9)
Setting each factor equal to zero, we get:
x = 0
x – 3 = 0, so x = 3
x^2 + 3x + 9 = 0, which has no real solutions (since the discriminant is negative)
Therefore, the solution set of the equation x^4 – 9x is 0, 3.
Nature of the Solution Set
The solution set of the equation x^4 – 9x is finite and real. This means that there are only a finite number of values that satisfy the equation, and all of those values are real numbers.
Graphical Representation, What is the solution set of x 4 9 x
The solution set of the equation x^4 – 9x can be represented graphically as follows:
[Image of a number line with points marked at x = 0 and x = 3]
The points on the number line represent the values of x that satisfy the equation.
Applications and Examples
The solution set of the equation x^4 – 9x is useful in a variety of applications, including:
- Finding the roots of a polynomial equation
- Solving problems in physics, such as projectile motion
- Solving problems in engineering, such as fluid dynamics
Popular Questions: What Is The Solution Set Of X 4 9 X
What is the definition of a solution set?
In mathematics, a solution set refers to the collection of all values that satisfy a given equation or system of equations.
How do you solve the equation x^4- 9x?
One method involves factorization: (x^2)(x^2 – 9) = 0. Solving each factor gives x = 0 or x = ±3.
What is the nature of the solution set for x^4- 9x?
The solution set is finite and consists of real numbers: x = 0, ±3.
