Prove, by considering the turning points on the graph \(y=x^3-3a^2x+b\) or otherwise, that if the equation \(x^3-3a^2x+b=0\) has three distinct real roots, then \(4a^6>b^2\).
Calculus meets Functions
Question
Prove, by considering the turning points on the graph \(y=x^3-3a^2x+b\) or otherwise, that if the equation \(x^3-3a^2x+b=0\) has three distinct real roots, then \(4a^6>b^2\).