Proving Cubic Equation Theta & a,b

In summary, The speaker is asking for help in solving a cubic equation with a given function. They have found a solution for a and b but need guidance on how to prove it mathematically. They also mention using the tangent of Theta to find values for a and b.
  • #1
agus
6
0
Hai, I have a question solving a cubic equation. I have a function
y=ax*x*x+bx*x. I want to get a solution for the value of a and b. From reference, I found that a=(xtan(Theta)-2y)/(x*x*x) and
b=(3y-xtan(Theta))/(x*x)
[Theta] is an angle or tangent of each point x along a cubic curve or function. Could anyone guide me on how to prove this statement mathematically?
TQ
 
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  • #2
You want to solve for a and b but you didn't provide any conditions on them.
 
  • #3
agus said:
Hai, I have a question solving a cubic equation. I have a function
y=ax*x*x+bx*x. I want to get a solution for the value of a and b. From reference, I found that a=(xtan(Theta)-2y)/(x*x*x) and
b=(3y-xtan(Theta))/(x*x)
[Theta] is an angle or tangent of each point x along a cubic curve or function. Could anyone guide me on how to prove this statement mathematically?
TQ

It is not at all clear what you want to do. Find values of a and b so that y= ax3+ bx2 has what properties??
 
  • #4
Well, anyway, from what you are saying, if we can choose values of X, just let X=1, giving Y=a+b. Then use a second value. Tangent of Theta? It might help to find out what that is.
 

1. How do you prove a cubic equation?

To prove a cubic equation, you must show that the equation can be expressed in the form of ax^3 + bx^2 + cx + d = 0, where a, b, c, and d are constants.

2. What is the role of theta in proving a cubic equation?

Theta (θ) is a variable that represents the roots of a cubic equation. It is used in the general solution of a cubic equation, which is x = -b/3a + (θ/a)^(1/3).

3. How do you determine the value of a, b, and c in a cubic equation?

The values of a, b, and c can be determined by comparing the given cubic equation with the general form of a cubic equation, ax^3 + bx^2 + cx + d = 0. From this, you can create a system of equations and solve for the values of a, b, and c.

4. What is the significance of a and b in a cubic equation?

The values of a and b determine the shape and position of the graph of a cubic equation. A positive value of a indicates a graph that opens upwards, while a negative value indicates a graph that opens downwards. The value of b determines the horizontal shift of the graph.

5. Can a cubic equation have more than three solutions?

No, a cubic equation can only have a maximum of three real solutions or roots. This is known as the fundamental theorem of algebra. However, the solutions can be repeated or complex numbers.

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