FP1 Topic 3: Complex numbers
Roots of quadratics 1
The quadratic equation ax^2+bx+c=0 has roots \alpha and \beta, therefore \displaystyle x^2+\frac{b}{a}x + \frac{c}{a} \equiv (x-\alpha)(x-\beta) therefore \displaystyle x^2+\frac{b}{a}x + \frac{c}{a} \equiv x^2-(\alpha+\beta)x+\alpha\beta therefore \alpha+\beta = -\displaystyle \frac{b}{a} and \alpha\beta = \frac{c}{a}

Summary This page uses jsMath. Note that you can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.