If a x 2 + b x + c = 0 and b x 2 + c x + a = 0 have a common root a ≠ 0, then a 3 + b 3 + c 3 a b c = Options: A . &nbsp1 B . &nbsp2 C . &nbsp3 D . &nbsp4

If ax2+bx+c=0 and bx2+cx+a=0 have a common root a ≠ 0, then a3+b3+c

Question

a x^{2} + b x + c = 0

and

b x^{2} + c x + a = 0

have a common root
a ≠ 0, then

\frac{a^{3} + b^{3} + c^{3}}{a b c} =

Options:

A . 1

B . 2

C . 3

D . 4

Answer: Option C
:
C
The condition for common roots gives

(b c - a^{2})^{2} = (c a - b^{2}) (a b - c^{2})

On simplification gives

a^{3} + b^{3} + c^{3} = 3 a b c

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