question_answer

The number of real values of k, such that the lines \[x-2y+3=0,kx+3y+1=0\]and \[4xky+2=0\] are concurrent, is

A)  0                    

B) 1

C) 2                     

D) infinite

Correct Answer: A

Solution :

[a] : Clearly, the lines will be concurrent if  \[\Rightarrow \]\[1(6+k)+2(2k-4)+3(-{{k}^{2}}-12)=0\] or\[3{{k}^{2}}-5k+38=0\]. No real roots since the discriminant is negative.