\(x^3-Ax+15\). Two of its real roots sum to 5. What is the absolute value of A?
An explanation would be greatly appreciated.
Thanks!
+128408
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
