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.

Options

A. a = b = c
B. `a = b ne c`
C. `a = -b = c`
D. none of these

Answer

1

Explanation

By observation x = -2 satisfies equation `x^(3) + 3x^(2) + 3x + 2 = 0`
then we have `(x + 2)(x^(2) + x + 1) = 0`
`x^(2) + x + 1 = 0` has nonreal roots.
Since nonreal roots occur in conjugate pair, `x^(2) + x + 1 = 0`
and `ax^(2) + bx + c = 0` are identical
`rArr a = b = c`