Learning math from tutoring

[jon_leonard]

I was recently helping a student with the rational-guesses trick to find the roots of a polynomial (ax^n ... b = 0 only has rational roots of the form +/- [factor of b]/[factor of a]).

She wound up asking what to do when none of the roots were real: Just try the same numbers with iThe answer, obvious in retrospect, is that instead of factoring

Comments

[helencoleman]

I wish I had your student. Mine have a hard time understanding that odd degree polynomials MUST have at least one real root.

[jon_leonard]

Oh, I didn't explain the parts about Gaussian integers to the student: I pondered the matter for a second or two, and told her that she'd always see a "hint" root in problems like that, and she didn't need to know more general techniques (they'd be something of a struggle for her). Very few of my students would benefit from that sort of digression, unfortunately.

But I learned something.