When there are no real roots, it does not mean there are no solutions to the equation. Just that the roots are imaginary. Your calculator shows you "i" as well. So what is "i"?

A brief introduction to imaginary numbers: http://www.mathsisfun.com/numbers/imaginary-numbers.html

solving equations with imaginary roots: http://www.regentsprep.org/regents/math/algtrig/ate3/quadcomlesson.htm

Video on binomial theorem, connection between binomial theorem and combinatorics: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/binomial_theorem/v/binomial-theorem-and-combinatorics-intuition

Exponential functions take on the form f(x) = ax, a > 0 and a not equal to 1.

ReplyDeleteWhy we let a > 0? What might happen if we allow a to be negative?

Imaginary numbers

ReplyDeleteWhen there are no real roots, it does not mean there are no solutions to the equation. Just that the roots are imaginary. Your calculator shows you "i" as well. So what is "i"?

A brief introduction to imaginary numbers: http://www.mathsisfun.com/numbers/imaginary-numbers.html

solving equations with imaginary roots: http://www.regentsprep.org/regents/math/algtrig/ate3/quadcomlesson.htm

This is a good guide to significant figures: http://www.usca.edu/chemistry/genchem/sigfig.htm

ReplyDeleteReal life applications of matrices (padlet class activity): http://padlet.com/madeleine_chew/wcub8owojch5

ReplyDeleteFor your reading pleasure =)

ReplyDeleteDigital Music Couldn't Exist Without the Fourier Transform: http://gizmodo.com/digital-music-couldnt-exist-without-the-fourier-transfo-1699155287

Hyperbola vs Parabola: http://www.differencebetween.net/science/difference-between-parabola-and-hyperbola/

ReplyDeleteFor your reading pleasure: Trigonometry and JPEG: http://petapixel.com/2015/05/24/how-jpeg-handles-colors-and-compression/

ReplyDeleteVideo on binomial theorem, connection between binomial theorem and combinatorics: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/binomial_theorem/v/binomial-theorem-and-combinatorics-intuition

ReplyDelete