This mistake fascinates me because there could be some underlying understanding: I have two of the four roots so the remaining polynomial is a quadratic. Or this kid could just be following several different procedures blindly: We wrote solutions in factored form, I can do that! Roots are when the function equals zero, I can write that! The quadratic formula is a way to find imaginary roots, I can solve that! Voila, problem solved.

It’s intriguing that the product (x-1)(x+5) sort of matches the first two terms, too. That gives one more reason to do this kind of crazy matching. Though the -5 from the product still ought to affect the 11x^2 in that case.

I also notice that the 64 isn’t squared, and the – should be on the initial 64, and that the roots of this quadratic would be real, so there’s something pretty big still missing in the answer-checking department as well as the application of the quadratic formula.

## 2 replies on “Imaginary Roots”

This mistake fascinates me because there could be some underlying understanding: I have two of the four roots so the remaining polynomial is a quadratic. Or this kid could just be following several different procedures blindly: We wrote solutions in factored form, I can do that! Roots are when the function equals zero, I can write that! The quadratic formula is a way to find imaginary roots, I can solve that! Voila, problem solved.

It’s intriguing that the product (x-1)(x+5) sort of matches the first two terms, too. That gives one more reason to do this kind of crazy matching. Though the -5 from the product still ought to affect the 11x^2 in that case.

I also notice that the 64 isn’t squared, and the – should be on the initial 64, and that the roots of this quadratic would be real, so there’s something pretty big still missing in the answer-checking department as well as the application of the quadratic formula.