Question

If

x^3+3x^2-9x+c

is of the form (x-α)^2 (x-β) ,

, then c is equal to​

Answer 1

Answer:

f(x)=x

3

+3x

2

−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.,

f(x)

′

=3x

2

+6x−9=0 has one root α,

Hence, x

2

+2x−3=0 or (x+3)(x−1)=0 has the root α.

Which can be either −3 or 1.

if α =1,

then f(x)=0

⟹1+3−9+c=0

⟹c−5=0

⟹c=5

If α=3 then,

f(x)=0

⟹−27+27+27+c=0

⟹c=−27