Tuesday

March 31, 2015

March 31, 2015

Posted by **Terri** on Sunday, December 12, 2010 at 11:50pm.

f(x)=12x^(3)-107x^(2)-15x+24

- repeat -
**TutorCat**, Monday, December 13, 2010 at 12:15amhttp://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut38_zero1.htm#step2

- pre-cal **need help for test in the morning -
**MathMate**, Monday, December 13, 2010 at 12:23amGiven:

f(x)=12x^(3)-107x^(2)-15x+24

Also if the leading coefficient (12) is positive, the function evaluates to -∞ at x=-∞ and to ∞ at x=∞. Thus it crosses the x axis at at least one place, or there is at least one real root.

In fact, application of Descarte's rule indicate that there are two changes of sign, so there are at least two positive roots. This also means that all three roots are real, since complex roots must come in pairs (conjugates).

Equate

f'(x)=36x²-214x-15

to zero, and solve for the maximum and minimum, if any.

f'(x)=0 at x=-0.07 and x=6.01

f(-0.07)=24.52 (maximum)

f(6.01)=-1326,

so there is a root close to 1 and probably another around -1.

By numerical methods, such as Newton's method, it should be possible to evaluate the zeroes as:

x=-0.531, x=0.417, and x=9.031

Check:

(x1*x2*x3)=2=24/12

(x1+x2+x3)=8.917 = 107/12

- pre-cal **need help for test in the morning -
**Terri**, Monday, December 13, 2010 at 12:25amThanks

**Answer this Question**

**Related Questions**

pre-cal - Find Zeros: F(x)=12x^3-107x^2-15x+24?

algbrea - 3x-5(3x-7)= 2(x+9) + 45 3x-15x+35= 2x+18 +45 -12x + 35 = 2x+63 -12x -...

Pre-Cal - Find the greatest integral upper bound of the zeros for the following ...

pre-cal - use the given zero to find the remaining zeros of the function. h(x)=x...

Pre-Calculus - Find all the rational zeros of the polynomial, and then find the ...

Pre-Cal. - Determine between which consecutive integers one or more real zeros ...

pre cal - Given f(x)=x^4-7x^3+18x^2-22x+12 A: list all possible rational zeros B...

pre-calc - How do I find all the real zeros of the polynomial function of these ...

pre-cal - Find the real zeros of f (x)= 2x^3 + 3x^2 – 8x + 3

pre-cal - Find the real zeros of f (x)= 2x^3 + 2x^3 – 8x + 3