3 What are all the roots of $$ x^{3}-3 x^{2}-x+3=0 $$ Whaice 1 point

Question

UpStudy AI · Accepted Answer

To find all the roots of the equation $$ x^{3} - 3x^{2} - x + 3 = 0 $$, follow these steps:

1. **Rational Root Theorem:** Possible rational roots are $$ \pm1, \pm3 $$.

2. **Testing Roots:**
   - **$$ x = 1 $$:**
     $$
     1^3 - 3(1)^2 - 1 + 3 = 1 - 3 - 1 + 3 = 0
     $$
     So, $$ x = 1 $$ is a root.

3. **Factor the Polynomial:**
   - Divide the polynomial by $$ (x - 1) $$:
     $$
     x^3 - 3x^2 - x + 3 = (x - 1)(x^2 - 2x - 3)
     $$
   
4. **Solve the Quadratic Equation:**
   - $$ x^2 - 2x - 3 = 0 $$
   - Factoring:
     $$
     (x - 3)(x + 1) = 0
     $$
     So, $$ x = 3 $$ and $$ x = -1 $$.

**All roots of the equation are $$ x = 1 $$, $$ x = 3 $$, and $$ x = -1 $$.**
The roots of the equation $$ x^{3} - 3x^{2} - x + 3 = 0 $$ are $$ x = 1 $$, $$ x = 3 $$, and $$ x = -1 $$.

3
What are all the roots of
Whaice 1 point

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions

3 What are all the roots of Whaice 1 point