If equations a x 2 + b x + c = 0 , a , b , c ∈ R , a ≠ 0 and 2 x 2 + 3 x + 4 = 0 have a common root, then a : b : c equals :

Step-by-step solution

a x 2 + b x + c = 0 ....(i) 2 x 2 + 3 x + 4 = 0 ....(ii) For equation (ii), D = 9 - 4 2 4 = - 23 < 0 Roots are complex conjugates. ⇒ Both roots are common in equation (i) and (ii). ∴    a 2 = b 3 = c 4 ⇒ a  :  b  :  c  : :  2  :  3  :  4