Questions: Find the real solutions of the following equation. 3x^3 + x^2 - 13x + 5 = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is □ (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions. Separate answers as needed. Type each answer only once.) B. The solution set is ∅.

$Find the real solutions of the following equation. 3x^3 + x^2 - 13x + 5 = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is □ (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions. Separate answers as needed. Type each answer only once.) B. The solution set is ∅.$

Transcript text: Find the real solutions of the following equation. \[ 3 x^{3}+x^{2}-13 x+5=0 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions. Separate answers as needed. Type each answer only once.) B. The solution set is $\varnothing$.

Solution

Solution Steps

Step 1: Identify the Polynomial Equation

We start with the polynomial equation: \[ 3x^3 + x^2 - 13x + 5 = 0 \]

Step 2: Find the Roots of the Polynomial

The roots of the polynomial are the solutions to the equation. The roots are: \[ x_1 \approx -2.4142, \quad x_2 \approx 1.6667, \quad x_3 \approx 0.4142 \]

Step 3: Verify the Real Solutions

All the roots obtained are real numbers. Therefore, the solution set consists of all these roots.