Polynomial questions

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May 10th 2011, 08:14 PM
MC Squidge

Polynomial questions

1. solve 3x^3-20x^2+33x-14<0

2. Find the formula of this graph

http://imageshack.us/m/841/9836/graphz.jpg
May 10th 2011, 09:05 PM
Sambit

1. $(3x-2)(x^2-6x+7)<0$
$(3x-2)[x-(3-\sqrt{2})][x-(3+\sqrt{2})]<0$
$(x-\frac{2}{3})[x-(3-\sqrt{2})][x-(3+\sqrt{2})]<0$
So $\frac{2}{3} , 3+\sqrt{2} , 3-\sqrt{2}$ are the points of interest.

$3-\sqrt{2}<x<3+\sqrt{2}, {x < 2/3}}$ is the solution.

2. I am not sure whether exact formula of the graph can be derived. However, you can find an approximate formula which satisfies some values of the graph http://en.wikipedia.org/wiki/Linear_interpolation
May 11th 2011, 04:21 AM
HallsofIvy

It appears from the graph that f(-2)= 0, f(3)= 0, and f(0)= 3 and there is a minimum at x= -2 so f'(-2)= 0. If that is right and we are allowed to assume this function is cubic, then write it as $f(x)= ax^3+ bx^2+ cx+ d$ and then $f'(x)= 3ax^2+ 2bx+ c$ . Put f(-2)= 0, f(3)= 0, f(0)= 3 into the first equation and f'(-2)= 0 into the second to get 4 equations to solve for a, b, c, and d.

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