If `x^(3)+3x^(2)-9x+lamda` is of the form `(x-alpha)^(2)(x-beta)` then `lamda` is equal to

Explanation

Here `x=alpha` is a repeated root of the equation f(x)=0.
Hence, `x=alpha` is also a root of the equation `f'(x)=0, i.e.,`
`3x^(2)+6x-9=0`
`"or "x^(2)+2x-3=0 or (x+3)(x-1)=0`
has the root `alpha` once which can be either -3 or 1.
`"If "alpha=1," then "f(x)=0" gives "-27+27+27+c=0`
`therefore" "c=-27`