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Sum and Product of Roots Question Help?

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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
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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

CPhill  Dec 12, 2017

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