Polynomial Equation Of Higher Degree

                    Lesson 1

                                                                                                                                                                          

                                                            Problem:                   Solve the equation:

x4 + 3x2 + 2 = 0

                                                             Solution                    (x2)2 + 3(x)2 +2=0

                           Step 1:  

                     

                                                                                Solution                          Letting x2 = a. Make the substitutions

                                                            Step 2:                                   a2 +2a + a 2 = 0

                                                                                                            (a + 2) (a + 1)

                                                            Solution                          Replace a with x2 and solve for the answers to the original equation

                                                             Step 3:                                   x2 + 2 = 0, x2 + 1=0 

                                                             Solution                          x=1; x= 2i

                                                             Step 4:

 

 Solution                    The answer is:  x= 1; x= 2i

 Step 5:                                                                      

 Complete                                                                   

                                                                                  

                                             

                                                             Try two practice problems:  

 

                                                                                               Solve:

 

A.

Solve the equation:

x4+6x2+9=0

 

B.

Find the zeroes of the function:

(x2-36)(x+7)=0

 

                                                                                               

        

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