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]?
The roots of the equation [math]x^2+3x-10=0[/math] are [math]\alpha[/math] and [math]\beta[/math], where [math]\alpha<\beta[/math]. An equation whose roots are [math]\alpha-1[/math] and [math]\beta+2[/math] is?