SOLUTION: If the equation (4+x)(6-x)=k has exactly one root, find this root. Thank you :)

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Question 1129277: If the equation (4+x)(6-x)=k has exactly one root, find this root. Thank you :)
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Under given conditions, the root of the equation is the point where the left side quadratic function achieves its maximum.


The roots of the left side polynomial are -4 and 6,

and the maximum of the quadratic function is achieved exactly at the midpoint between them.


So, the only root of the equation is x= %28-4+%2B+6%29%2F2 = 1.     Answer

Solved.