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\(x^3-Ax+15\). Two of its real roots sum to 5. What is the absolute value of A?

 

An explanation would be greatly appreciated.

 

Thanks!

Guest Dec 12, 2017
 #1
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+1

 

Writing this in the form  ax^3  + bx^2  + cx + d

 

a = 1      b  = 0       c  = -A   and   d   =  15

 

The sum of the roots   =    -b/a  =  0

 

So .....if two of the real roots sum to 5, the other root must be  -5

 

Using synthetic division, we have that

 

 

 

-5  [  1     0     -A      15            ]

              -5    25      -125 + 5A

        ____________________

         1    -5   25-A    -110  +  5A

 

 

So.....if -5 is a root.....-110 + 5A  = 0

 

-110 + 5A  = 0

 

5A  =  110

 

A  =  22

 

So      l  A   l       =    22

 

Look at the graph of   x^3 - 22x + 15   here :

 

https://www.desmos.com/calculator/k6pz3xpcj2

 

Note that one root  = -5 and the other two sum to 5

 

 

cool cool cool

CPhill  Dec 12, 2017

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