+0  
 
0
3
3
avatar+33 

Find all roots of the polynomial
\(P(x) = 4x^3 - 11x^2 + 2x + 3.\)

 Jun 22, 2024
 #1
avatar+129725 
+1

4x^3 -11x^2 + 2x + 3

 

Test whether 3/4  is a root

 

 

3/4  [  4     -11     2      3   ]

                    3   -6      -3

   ___________________

        4       -8     -4      0

 

It is  a root

 

The remaining polynomial is

 

4x^2 - 8x - 4 = 0

 

x^2 -2x - 1  =0

 

x^2  -2x   =  1

 

x^2 -2x +1  =1 + 1

 

(x -1)^2  = 2       take both roots

 

x -1  =sqrt 2                   x - 1 = -sqrt 2

 

x = 1 + sqrt 2                 x = 1 - sqrt 2

 

These are the other two roots

 

cool cool cool

 Jun 22, 2024
 #2
avatar+33 
+1

Thanks! The detailed explanation really helps.

MeldHunter  Jun 22, 2024
 #3
avatar+129725 
0

No prob !!!

 

cool cool cool

CPhill  Jun 22, 2024

2 Online Users

avatar