Solving Polynomial Equations (AQA A-Level Further Maths): Flashcards

If $z = a + bi$ is root, $z^* = a - bi$ also root (real coeffs)

Complex/imaginary

$z^* = a - bi$

Always real

Always real

In conjugate pairs

Complex roots in pairs; can't have exactly 3 complex

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Use conjugate pair; both roots needed

$x^2 - (\alpha + \beta)x + \alpha\beta = 0$