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Missing root when solving equation in sageMath

asked 2018-07-17 18:58:17 -0500

Sam Tan gravatar image

updated 2018-07-17 19:28:53 -0500

tmonteil gravatar image

When I solve equation using sageMath, it missed one root.

sage: solve([4/5*(x - 1)^2/x^(1/5) + 2*(x - 1)*x^(4/5)==0] ,x)

[x == (2/7), x == 1]

The equation has 3 roots. It misses x==0.

What is the reason?

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answered 2018-07-17 19:29:59 -0500

tmonteil gravatar image

updated 2018-07-17 19:32:03 -0500

Because of the denominator x^(1/5), the function you are considering is not defined at $x=0$. You can have a look at its plot to get convinced:

sage: f = 4/5*(x - 1)^2/x^(1/5) + 2*(x - 1)*x^(4/5)
sage: f.plot(0,1)
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Asked: 2018-07-17 18:58:17 -0500

Seen: 19 times

Last updated: Jul 17