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Answer 1 · 2018-01-04T14:02:02

#:. n=4, or, n=-2#.

Given that, the point #(2,-6)# is on the graph of the function

#P(x)=x^3+nx^2-n^2x+2#, means that, #P(2)=-6#.

#:. 2^3+n*2^2-n^2*2+2=-6#,

#:. 8+4n-2n^2+2=-6, i.e., #

# 2n^2-4n-16=0, or, #

# n^2-2n-8=0#.

#:. (n-4)(n+2)=0#,

#:. n=4, or, n=-2#.