A) 1
B) 7
C) \[-7\]
D) 7 or \[-7\]
Correct Answer: D
Solution :
Given equation is \[{{x}^{2}}+px+12=0\] Now, if a and b are its roots, then Sum of roots, \[a+b=-p\] and Product of roots, \[a\times b=12\] Also, \[a-b=1\] (Given) We know that, \[{{(a-b)}^{2}}={{(a+b)}^{2}}-4ab\] \[\Rightarrow \] \[1={{p}^{2}}-4\times 12\,\,\,\,\,\,\Rightarrow \,\,\,\,1={{p}^{2}}-48\] \[\Rightarrow \] \[{{p}^{2}}=49\,\,\Rightarrow \,\,\,\,=\pm 7\]
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