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If a1x^2 + b1 x + c1 = 0 and a2x^2 + b2...

If `a_1x^2 + b_1 x + c_1 = 0` and `a_2x^2 + b_2 x + c_2 = 0 ` has a common root, then the common root is

A

`alpha = (c_(1)a_(2) - c_(2)a_(1))/(a_(1)b_(2)-a_(2)b_(1)) = (b_(1)c_(2)-b_(2)c_(1))/(c_(1)a_(2)-c_(2)a_(1))`

B

`alpha = (c_(1)a_(2) - c_(2)a_(1))/(a_(1)b_(2)-a_(2)b_(1)) = (b_(1)c_(2)-b_(2)c_(1))/(c_(1)a_(2)-c_(2)a_(1))`

C

the condition for one common root is `(c_(1)a_(2)+c_(2)a_(1))^(2)=(a_(1)b_(2)-a_(2)b_(1))(b_(1)c_(2)-b_(2)c_(1))`

D

The condition for one common root is `(a_(1)b_(2)-b_(1)a_(2))^(2) = (c_(1)a_(2) - a_(1)c_(2)) (b_(1)c_(2) - b_(2)c_(1))`

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