Given that one of the values of \(x\) satisfying the quadratic equation \[x^2-(2a+1)x+(a^2+2)=0\] is twice the other, find \(a\).
If we know the values of \(x\) that satisfy a quadratic equation, how can we use this to write the equation down?
Could we now compare our equation with the one given?
The green curve here is \(y=x^2-(2a+1)x+(a^2+2)\).
The blue line segment \(OP\) represents the smaller root, and the length \(OP'\) is double \(OP\).