Solving cubic equations using calculator

skipjack

Forum Staff
Dec 2006
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For the example you gave, 250 isn't a root.
 

skeeter

Math Team
Jul 2011
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Texas
This polynomial equation below, I solved using TI-82 and I only got one root:
\(\displaystyle 4x^3-16000x^2+16*10^6x-3072*10^3=0\)
so got the first root as 250. How do I find the other ones, or use this root to find out other ones?
As skipjack stated, x=250 is not a root.

Note the polynomial's coefficients are all divisible by 4, yielding the equation

$x^3-4000x^2+(4\times10^6)x-738\times10^3$

I used a TI-84 emulator (same solve feature as an 82)

first root calculated from the default guess, x=0

root1.png

second root required a guess of x=1000

root2.png

third and final root used a guess of x=2500

root3.png
 

skeeter

Math Team
Jul 2011
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$4(251)^3 - 16000(251)^2 + 16000000(251) - 3072000 = 3068165004$

check it yourself ...
 
Jun 2019
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Hawk, your link has the $x^0$ coefficient as 3 billion, not 3 million. Also, the root was only approximately 251. It seems nitpicky, but in some cases a small error in the root in your denominator can produce large errors in the subsequent roots.
 

skipjack

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Dec 2006
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$4x^3 - 16000x^2 + 16*10^6x - 3072*10^6 = 4(x - 1200)(x^2 - 2800x + 640000)$
 

skipjack

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Dec 2006
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Its value was changed in Hawk's later post (#14).