Flashcards
Polynomials
Cards in this deck (6)
- 1Any quadratic with real coefficients has what 3 possible sets of roots?-2 real
-2 repeated
-2 non real (complex conjugates) - 2What method can be used to expand complex conjugates into quadratics? (e.g. (z-(3+2i))(z-(3-2i)) )z^2 - (sum of roots) + (product of roots) = 0
(note if it was for example 2z^2 then you would have to divide everything by 2 to get z^2 on its own) - 3How would we factorise x^2+4?(x+2i)(x-2i)
- 4Cubics with real coefficients have how many real roots?At least 1, which we can find using the factor theorem and use it to take out linear factor leaving a more solvable quadratic
- 5Quartics with 2 non real roots are what?Complex conjugates
- 6Quartics with no real roots have what?2 pairs of 2 complex numbers
(each quadratic factor has its own conjugates of each other)