# WolframAlpha Returns only 2 Roots for a Polynomial Equation of 6 Degree

I think this is really weird.

I want to solve the following equation:

$$(2x^2+3x+5)^3+(2x^2+3x+5)^2=0$$

This is a polynomial equation of 6 degrees. It should have 6 roots.

But wolframalpha only returns 4 roots! Anything I miss?

This is the command I use:

solve ((2x^2+3x+5)^3)+((2x^2+3x+5)^2)=0


Edit: Ah, Wolframalpha doesn't return repeated roots. So now case solved.

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Maybe the roots are equal, you have something like (degree 2)^n – Ronaldo Sep 28 '10 at 12:57
I think you're missing the fact that $x^2+3x+5=x^2+3x+5,$ as both terms in your brackets are equal. However, are you sure this is what you meant to type as you have $2x^2+3x+5$ in the command line you used in wolframalpha? – Derek Jennings Sep 28 '10 at 13:04
It's actually a decic (tenth-degree) that you have; with two roots of multiplicity 5. – J. M. Sep 28 '10 at 13:08
@J.M., there is a typo, which I have fixed. – Graviton Sep 28 '10 at 13:09
You still have the same expression in each bracketed term, even after the edit, so just write $(2x^2+3x+5)^5=0,$ and you should see what's happening. – Derek Jennings Sep 28 '10 at 13:11

Solve[(2x^2 + 3x + 5)^3 + (2x^2 + 3x + 5)^2 == 0, x]