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How would you solve for the x-intercept of this equation?
y = (x^3) - ( 4x^2 ) + 6
If you want to use other numbers that is fine, I just want an idea of how this would be done
I understand that you set y = 0.
What I need help wit s the x^3 and the x^2
1 Answer
- anonymousLv 710 years agoFavorite Answer
For quadratics, there is the quadratic formula. For polynomials of degree 3 and 4, there are formulas to find the roots, but they are extremely complicated. For polynomials of degree 5 or higher, there is no such formula. [The last sentence was proved in 1824 by Norwegian mathematician Niels Abel.] So, in general, one must use various means to attempt to determine the roots of the higher-level polynomials.
For instance, using your example function, I would :
1) Sketch the graph of the function by plotting various points (nowadays you could just graph it in seconds using a graphing calculator or a spreadsheet program). That will give you a rough idea of where the real roots are. (Sometimes there can be imaginary, complex roots.)
2) Then I would use Newton's method to get a value for each of the roots to the desired level of precision.
