Finding roots

I'm not sure if this is the right forum, but this was in my calculus class.

$\displaystyle f(x) = (16x+50x^3) - 40^3$

I need to find the roots. And I want to find the precise roots, without a decimal.

Guess and check, and graphing result in a root of ~10.845

make $\displaystyle f(x)=0$, so $\displaystyle 0= (16+50x^3)-40^3$

$\displaystyle 0= (16+50x^3)-64000$

$\displaystyle 0= 50x^3-63984$

Now solve for x.

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Originally Posted by ankhmor

I'm not sure if this is the right forum, but this was in my calculus class.

$\displaystyle f(x) = (16x+50x^3) - 40^3$

I need to find the roots. And I want to find the precise roots, without a decimal.

Guess and check, and graphing result in a root of ~10.845

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Why, where has this come from and are you sure that you have posted it correctly?

If you want the closed form roots of what you have posted you will need to use Cardarno's method for the roots of the depressed cubic, which is about halfway down >>this<< page

CB

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Originally Posted by pickslides

make $\displaystyle f(x)=0$, so $\displaystyle 0= (16+50x^3)-40^3$

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pickslides, the equation was $\displaystyle (16x+ 50X^3)- 40^3= 0$ which becomes
50x^3+ 16x- 64000= 0, rather more difficult to solve.

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$\displaystyle 0= (16+50x^3)-64000$

$\displaystyle 0= 50x^3-63984$

Now solve for x.

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