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If x^3+3x^2-9x+c is of the form (x-alpha...

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

A

27

B

`-27`

C

5

D

-5

Text Solution

Verified by Experts

The correct Answer is:
B, C
Since `f(x)=x^(3)+3x^(2)-9x+lamda=(x-alpha)^(2)(x-beta)`
`:.alpha`is a double root.
`:.f'(x)=0` has also one root` alpha`.
`:.x^(2)+2x-3=0` or `(x+3)(x-1)=0`
has the root `alpha` which can either `-3` or 1.
If `alpha=1` then `f(1)=0` gives `lamda-5=0implieslamda=5`
If `alpha=-3`, then `f(-3)=0` gives
`-27+27+27+lamda=0`
`implieslamda=-27`
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