Given:
[tex]f(x)=x^3+3x^2-5x-4[/tex]
To determine the roots, we let f(x)=0 first:
[tex]x^3+3x^2-5x-4=0[/tex]
Next, we find factor of the equation:
[tex]\begin{gathered} x^3+3x^2-5x-4=(x+4)(x^2-x-1)=0 \\ \end{gathered}[/tex]
Then, we use quadratic formula for x^2-x-1=0:
We plug in what we know:
Hence,
We also get the x value of x+4=0:
[tex]\begin{gathered} x+4=0 \\ x=-4 \end{gathered}[/tex]
Therefore, the answer is:
