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About Josh
Expertise
When I work through problems, I emphasize principles and key ideas which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponentials & Logarithms. Basic Calculus. Probability, Permutations and Combinations. Mathematical Induction. Complex numbers. Physics problems.
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Experience:
I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.
Supplementary Website:
See a selection of past questions in my maths repository under "Question Archive"
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Bachelor degree in Engineering Science.
"Everyone struggles with something."
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You are here: Experts > Science > Math for Kids > Basic Math > algebra 3
Expert: Josh - 10/13/2009
Question
i need help on this problem.dont understand where to start
x^3+6x^2-4x-24=o
finding the real number solution of the equation
Answer
Alexis,
This question basically asks us to find all possible values of x which make the equation true. There are at most 3 unique solutions (also called "zeros" or "roots") because this is a third order polynomial.
Factorization is the key to this problem. To get anywhere, we need to make these observations.
Observe that we may rearrange the equation as
x^3-4x + 6x^2-24 = 0
Then, we can factorize the 1st and 2nd term, and separately for the 3rd and 4th term.
x(x^2-4) + 6(x^2-4) = 0
Now, since the quadratic factor (x^2-4) is repeated, we can pull this out the front and use it as a common factor. Therefore,
(x^2-4)(x+6)=0 ...[*]
Now, recognize that x^2-4 is a "difference of square" expression. In general, x^2-a^2 = (x+a)(x-a). So, we can decompose [*] further as
(x+2)(x-2)(x+6)=0.
Once we reach this point, finding the solutions is easy. The expression equals zero when either (x+2)=0, (x-2)=0 or (x+6)=0. These occur precisely when x=-2, x=+2 and x=-6. These are the solutions.
Good luck and practice heaps.
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