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

Question 1129277: If the equation (4+x)(6-x)=k has exactly one root, find this root. Thank you :)
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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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=  = 1.     Answer

Solved.

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