With three sub-questions, but only need help for the last two 
(comes under the sub-heading of turning points)
Show that x^3 + ax + b = 0 has:
(a) only one real root if a >0.
(b) two equal roots if 4a^3 + 27b^2 = 0
(c) three distinct roots if 4a^3+27b^2 < 0
I'm confused as to where the 4a^3 + 27b^2 comes from. Any help would be appreciated!
By the way, in the rare case that anyone is familiar with the Australian curriculum, this comes under high school Extension 2 Maths in NSW.
(comes under the sub-heading of turning points)
Show that x^3 + ax + b = 0 has:
(a) only one real root if a >0.
(b) two equal roots if 4a^3 + 27b^2 = 0
(c) three distinct roots if 4a^3+27b^2 < 0
I'm confused as to where the 4a^3 + 27b^2 comes from. Any help would be appreciated!
By the way, in the rare case that anyone is familiar with the Australian curriculum, this comes under high school Extension 2 Maths in NSW.