Discover the Easy Way to Find the X-Intercept for x^3-6x^2-15x+4

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In summary, finding the x-intercepts for a cubic equation involves solving for the roots of the equation, either by using a program like Mathematica or by using the cubic formula. Another method, known as Newton's method, involves finding the derivative and solving for x. However, there is no simple or trivial way to find the x-intercepts for a cubic equation. The most efficient method is to plug in the coefficients into the cubic formula.
  • #1
gr3g1
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Hey, Is there any simple way of finding the x intercept for

x^3-6x^2-15x+4
 
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  • #2
Basically find the roots of the equation?
I bet you already know that there are three roots.
to solve for x in a cubic of form ax^3+bx^2+cx+d, use a program like mathematica, or check out this cubic forumla:

http://www.math.vanderbilt.edu/~schectex/courses/cubic/cubic.gif

plug in 1 for a, 6 for b, 15 for c, and 4 for d.
pretty long, but it always works.
 
Last edited:
  • #3
As above, the only way to find the x-intercepts is to set y= 0 and solve the equation. This equation has no rational roots so there is no "simple" way to do it.
 
  • #4
About newtowns method?
 
  • #5
what about it? [tex] x_{n+1} = x_n - \frac {f(x_n)}/{f'(x_n)} [/tex]
find the derivative, and start solving...edit:

there's supposed to be a "x_n - "before the fraction, but it isn't showing up...
 
  • #6
Thats another way of finding the x intercepts? Right?
(Our teacher never mentioned it, i think I am going to have to learn it myself)
 
  • #7
Finding the x-intercepts for
x is exactly the same as finding the solutions to
x^3-6x^2-15x+4= 0. There is no "trivial?" way of doing that.
 

FAQ: Discover the Easy Way to Find the X-Intercept for x^3-6x^2-15x+4

1. What is the X-intercept of the equation x^3-6x^2-15x+4?

The X-intercept is the point where the graph of a function crosses the x-axis. In the given equation, it is the value of x where the y-coordinate is equal to 0.

2. How do I find the X-intercept for x^3-6x^2-15x+4?

To find the X-intercept, set the equation equal to 0 and solve for x. This can be done by factoring, using the quadratic formula, or using synthetic division.

3. Can I use any method to find the X-intercept for x^3-6x^2-15x+4?

Yes, you can use any method that you are comfortable with and that gives you the correct answer. However, some methods may be more efficient than others.

4. Is finding the X-intercept important in mathematics and science?

Yes, finding the X-intercept is important in many fields of mathematics and science. It helps us understand the behavior of functions and can be used to solve real-world problems.

5. Are there any shortcuts or tips for finding the X-intercept for x^3-6x^2-15x+4?

Yes, there are some shortcuts and tips that can make finding the X-intercept easier. For example, if the given equation is of the form ax^3+bx^2+cx+d, you can first divide all coefficients by a to make the leading coefficient equal to 1. This can make factoring or using the quadratic formula simpler. Additionally, looking for common factors and using the rational root theorem can also be helpful.

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