A) 3
B) 4
C) 5
D) none of these
Correct Answer: B
Solution :
| \[x=\frac{p}{p-15}\] |
| \[x=1+\frac{p}{p-15}\] ?(1) |
| Roots are positive \[\Rightarrow \] \[\frac{p}{p-15}>0\] |
| i.e. \[p\in (-\,\infty ,\,\,0)U(15,\,\,\infty )\] But \[p\in N\] \[\therefore \] \[p\in (15,\,\,\infty )\] |
| From (1), For x to be integer \[\frac{15}{p-15}\] should be integer, it is possible |
| When \[0<p-15\le 15\] or \[0<p\le 30\] But \[p>15\] |
| \[\therefore \]\[p\in (15,\,\,30]\] |
| so \[p=16,\] 18, 20, 30 |
| \[\therefore \]No. of positive integral roots are 4. |
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