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If equations $\;ax^{2}+bx+c=0\;, (a,b,c \in R\;, a \neq 0)\;$ and $\;2x^{2}+3x+4=0\;$ have a common root then $\;a : b: c\;$ equals :

$(a)\;1: 2 :3 \qquad(b)\;2: 3 :4\qquad(c)\;4: 3 :2\qquad(d)\;3: 2 :1$

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D of equation 2x^2+3x+4=0    is less than zero. Hence root are complex and conjugate.

Hence both root must be common.  (b) is correct.
answered Apr 2, 2015 by Limitsofawesomeness

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