Questions: 5x^3 - 27x^2 - 17x - 6 = 0

Transcript text: $5 x^{3}-27 x^{2}-17 x-6=0$

Solution

Step 1: Identify the Roots

The cubic equation given is:

\[ 5x^3 - 27x^2 - 17x - 6 = 0 \]

The roots of this equation are:

\[ x_1 = 6.0000 \] \[ x_2 = -0.3000 + 0.3317i \] \[ x_3 = -0.3000 - 0.3317i \]

Step 2: Classify the Roots

The roots can be classified as follows:

One real root: $ x_1 = 6.0000 $
Two complex conjugate roots:
- $ x_2 = -0.3000 + 0.3317i $
- $ x_3 = -0.3000 - 0.3317i $

The real root is:

\[ \boxed{x = 6.0000} \]

The complex roots are:

\[ \boxed{x = -0.3000 + 0.3317i} \] \[ \boxed{x = -0.3000 - 0.3317i} \]

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