Respuesta :
Correct answer is C.
[tex]-5 x^3 + 9 x^2 +12 x+ 2=(-5 x-1) \left(x^2-2 x-2\right) \\ \\\left\{-\frac{1}{5},1-\sqrt{3},1+\sqrt{3}\right\}\to \{-0.2,-0.732051,2.73205\}[/tex]
Or check if f(0.2) = 0 to eliminate A and B.
Then check if f(-0.5) = 0 to eliminate D.
[tex]-5 x^3 + 9 x^2 +12 x+ 2=(-5 x-1) \left(x^2-2 x-2\right) \\ \\\left\{-\frac{1}{5},1-\sqrt{3},1+\sqrt{3}\right\}\to \{-0.2,-0.732051,2.73205\}[/tex]
Or check if f(0.2) = 0 to eliminate A and B.
Then check if f(-0.5) = 0 to eliminate D.