I've been given the following problem and I can't seem to figure out the solution, would appreciate any help and direction to solution !
Let's look at the equation : y3 + py + q = 0 (*)
We shall define Delta (or d in short) d = 4p3 + 27q2Prove that :
a) If d > 0 , then (*) has a single solution .
b) If d = 0 , and at least one of the coefficients (p , q) =/= 0, then (*) has 2 solutions .
c) If d < 0 , then (*) has 3 solutions .
Thank you very much in advance !
Let's look at the equation : y3 + py + q = 0 (*)
We shall define Delta (or d in short) d = 4p3 + 27q2Prove that :
a) If d > 0 , then (*) has a single solution .
b) If d = 0 , and at least one of the coefficients (p , q) =/= 0, then (*) has 2 solutions .
c) If d < 0 , then (*) has 3 solutions .
Thank you very much in advance !