Solving Polynomials
- Know that non-real roots of polynomial equations with real coefficients occur in conjugate pairs.
- Calculate complex solutions to quadratic equations by completing the square.
- Compare and contrast quadratic equations with real and with non-real complex solutions.
- Justify that a quadratic equation will have either real or non-real solutions using graphical reasoning.
- Solve any quadratic equation with real coefficients.
- Solve cubic or quartic equations with real coefficients (given sufficient information to deduce at least one root for cubics or at least one complex root or quadratic factor for quartics).