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Q.
The set of real value(s) of $p$ for which the equation, $|2 x +3|+|2 x -3|= px +6$ has more than two solutions is :
Complex Numbers and Quadratic Equations
Solution:
Draw graphs of :
and $ y=p x+6$
From the graph it is obvious that if, $p =0$ we have infinite solutions ranging from $\left[-\frac{3}{2}, \frac{3}{2}\right]$ if $0< p< 4$ or $-4< p< 0$, two solutions, if $p =4$ or -4 we have $x =0$ is the only solution
