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 :

Question

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 : (A) (0,4] (B) (-4,4) (C) R - 4,-4,0  (D)  0

Tardigrade Admin · Accepted Answer

Draw graphs of:

and y=p x+6 From the graph it is obvious that if, p =0 we have infinite solutions ranging from [-(3/2), (3/2)] if 0< p< 4 or -4< p< 0, two solutions, if p =4 or -4 we have x =0 is the only solution

Q. The set of real value(s) of $p$ for which the equation, $∣2 x + 3∣ + ∣2 x - 3∣ = p x + 6$ has more than two solutions is :

$(0, 4]$

$(- 4, 4)$

$R - {4, - 4, 0}$

${0}$

Draw graphs of :

and $y = p x + 6$
From the graph it is obvious that if, $p = 0$ we have infinite solutions ranging from $[- \frac{3}{2}, \frac{3}{2}]$ if $0 < p < 4$ or $- 4 < p < 0$ , two solutions, if $p = 4$ or -4 we have $x = 0$ is the only solution

Q. The set of real value(s) of p for which the equation, ∣2x+3∣+∣2x−3∣=px+6 has more than two solutions is :

(0,4]

(−4,4)

R−{4,−4,0}

{0}