Complex roots of quadratic equationsEdexcel International A Level Further Maths: Mind map

Exam questions on Complex roots of quadratic equations

1. The quadratic equation $z^2-6z+13=0$.
   The equation $z^2+kz+13=0$, where $k$ is a real constant, has no real roots. Find the range of possible values of $k$.2 marks
2. The quadratic equation $z^2+4z+29=0$.
   Show that $z=-2+5\mathrm{i}$ satisfies the equation.2 marks
3. The quadratic equation $2z^2-6z+5=0$.
   Solve the equation, giving the roots in the form $p+q\mathrm{i}$.3 marks