If x3+3x2−9x+c is of the form (x−α)2(x−β), then c is equal to
27
-27
5
-5
f(x)=x3+3x2−9x+c is of the form (x−α)2(x−β), showing that α is a double root so that f(x) = 0 has also one root α, i.e., 3x2+6x−9=0 has the root α which can be either -3 or 1. If α=1, then f(x)=0 gives c−5=0 or c=5. If α=−3, then f(x) = 0 gives −27+27+27+c=0∴ c=−27