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I answered a nice question on WyzAnt about approximating roots to a quadratic equation that had real but irrational roots.     Calculus enables us to find rational approximations to these irrational roots.  I will re-present the solution to the problem, and continue to find a general expression to do this for an arbitrary polynomial.   "Problem: approximate roots of -9x^2+8x+5.   There is a nice approach using calculus to estimate/approximate a function without a square root and calculator. We can use the concept of moments to get an approximation to a function. For this example, we have a quadratic function in (x) with coefficients, a=-9, b=8, and c=5, as indicated in a previous solution. Thus f(x)=ax^2+bx+c. First we need to find a general idea of where a root (an x where f(x)=0) is located. To do this we can check the value of the function for some easy numbers, x=0 and x=1 are always... read more

MP3 players example   The profit in millions of dollars for an MP3 player can be done with the polynomial P=-4x^3 + 12X^2 + 16X. X represents the number of MP3 players produced annually. The company currently produces 3 million MP3 players and makes a profit of $ 48,000,000. To figure out the least amount of MP3 players the company can produce and still make the same profit we need to solve for P.   Step 1 Set P=48 This represents the total profit. 48=-4X^3 + 12X^2 + 16X   Step 2 subtract the 48 from 48 and from the end of the equation, like this 48=-4X^3 + 12X^2 + 16X - 48                                                                                                    ... read more

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