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If the equations a x^2+b x+c=0 and x^3+3...

If the equations `a x^2+b x+c=0 and x^3+3x^2+3x+2=0` have two common roots, then a. `a=b=c` b. `a=b!=c` c. `a=-b=c` d. none of these.

A

`a = b ne c`

B

`a = -b = c`

C

`a = b = c`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `x^(3) + 3x^(2) + 3x + 2 = 0`
`rArr" "(x+2)(x^(2)+x+1)=0 rArr x = -2, omega, omega^(2)`.
It is given that `ax^(2) + bx + c = 0 and x^(3) + 3x^(2) 3x + 2 = 0` have two common roots. Therefore, `omega and omega^(2)` are the common roots.
Hence, a = b = c = 1.
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