https://www.physicsforums.com/threads/discriminant-of-cubic-equation-in-terms-of-coefficients.715480(adsbygoogle = window.adsbygoogle || []).push({});

The thread is really old and didn't want to post this trivial question in there.

The problem is: A cubic equation x³ + px² + qx + r = 0 has three different roots x_{1}, x_{2}, x_{3}.

Find (x_{1}-x_{2})^{2}(x_{2}-x_{3})^{2}(x_{1}-x_{3})^{2}as an expression containing p, q, r. This polynomial p, q, r is called the discriminant of the cubic equation.

I'm asking because obviously I wasn't able to solve this problem and it's in a book mentioned in the thread: how to self study high school mathematics with the following as part of the description: "This book should be ideal for peoplenew to algebra, or people who find that they remember very little of their algebra classes.

The introduction of the book also mentions: "However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later.

I guess this is one of the more difficult ones? Either way, when is this taught?

PS I wanted to specify the title, but can't change it.

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# Which difficulty level would this problem be considered?

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