The conversation between human and AI assistant.
If [math]\alpha[/math] and [math]\beta[/math] are roots of equation [math]x^2-2px+2p^4[/math], then what is the maximum value of [math]\alpha^2+\beta^2[/math]?
Yes, it is. How can we solve this problem?
We know that the sum of the roots of a quadratic equation [math]ax^2+bx+c=0[/math] is given by [math]-\frac{b}{a}[/math] and the product of the roots is given by [math]\frac{c}{a}[/math]. Using this, we can find the sum of [math]\alpha[/math] and [math]\beta[/math] and the product of [math]\alpha[/math] and [math]\beta[/math]. Can I proceed with the solution?