<s>[INST] Determine the number of real roots in the equation... Determine the number of real roots in the equation $2x^3 + x^2 = 3$.
I know about finding the different roots, and solving giving that it has (for example) 2i as a root, but I'm not sure how to just find the amount of real roots. 
I've found nothing that can help so far. 
 [/INST] HINT:
$$2x^3+x^2-3=2(x^3-1)+(x^2-1)=2\{(x-1)(x^2+x+1)\}+(x-1)(x+1)$$
$$=(x-1)\{2(x^2+x+1)+x+1\}=(x-1)(2x^2+3x+3)$$
Alternatively,  using Remainder Theorem, $(x-1)|(2x^3+x^2-3)$
So, by actual division $2x^3+x^2-3=(x-1)(2x^2+3x+3)$
Do you know how to determine the nature of a Quadratic Equation? 
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