Stage: 5 Challenge Level:
This Hint is for students who have only recently met complex
What can you say about the product of the roots of the quadratic
equation $x^2 + px + q = 0$?
If the roots of this quadratic equation, where $p$ and $q$ are real
coefficients, are the complex numbers $z_1$ and $z_2$ explain why
$z_1$ and $z_2$ are complex conjugates.
Explain why the square of the distance from the origin of the point
$u+iv$ in the Argand diagram is given by the product of complex
What does this tell you about the locus of the complex roots of
$x^2 +px +q = 0$ as you change $p$ keeping $q$ constant?
Was your conjecture correct?