Exercise 3.  Find all solutions to the following depressed cubics.  
3 (a).  .   

Solution 3 (a).

See text and/or instructor's solution manual.

To solve .  

The depressed cubic equation is

The problem at hand is

We identify the coefficients b and c.

Substitute these values into the formula  

Get  .

Now factor   out of the cubic.  

    

Use the quadratic equation and solve  .

We are done.  The roots are   .

Aside.  We can let Mathematica double check our work.

An equivalent monic polynomial is  .

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell