The solution to the problem is as follows:
x³ + x² − 6x = 0
x (x² + x − 6) = 0
x (x − 2) (x + 3) = 0
x = 0, 2, −3
f(x) = 2x³ + 5x² + 6x − 4
f(−x) = −2x³ + 5x² − 6x − 4
Let's look at signs only and how many sign changes there are:
f(x) = + + + −
1 sign change ----> 1 positive root
f(−x) = − + − −
2 sign changes ----> 2 or 0 negative roots
Min. number of real roots = 1 ----> max. number of complex roots = 2
Max. number of real roots = 3 ----> min. number of complex roots = 0
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