A) \[\pm 6\]
B) \[\pm 2\]
C) \[2,-6\]
D) \[6,2\]
Correct Answer: A
Solution :
Let roots of the equation\[{{x}^{2}}+px+8=0\]are\[\alpha \]and\[\beta ,\]then \[\alpha +\beta =-p\] and \[\alpha \beta =8\] Also given, \[\alpha -\beta =2\] \[\Rightarrow \] \[\sqrt{{{(\alpha +\beta )}^{2}}-4\alpha \beta }=2\] \[\Rightarrow \] \[{{(-p)}^{2}}-4\times 8=4\] \[\Rightarrow \] \[{{p}^{2}}=4+32\] \[\Rightarrow \] \[p=\pm 6\]
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