question_answer

For a quadratic polynomial \[p(x)={{x}^{2}}-8x+15\] for all \[x\in r,\] which one among the following can be true?

A) \[p(x)\ge 0,\] when \[3\le x\le 5\] and \[p(x)\le 0,\] when \[x\le 3\] or \[x\le 5\]

B) \[p(x)\ge 0,\] when \[-\,3\le x\le -\,5\] and \[p(x)\le 0,\] when \[x\le -3\] or \[x\ge -\,5\]

C) \[p(x)\ge 0,\] when \[x\le 3\] or \[x\ge 5\] and \[p(x)\le 0,\] when \[3\le x\le 5\]

D) \[p(x)\ge 0,\] when \[x\le -\,3\] or \[x\ge -\,5\] and \[p(x)\le 0,\] when \[-\,5\le x\le -\,3\]

E)  None of these