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Question

If (x2+x+3)2−(p−3)(x2+x+3)(x2+x+2) +(p−4)(x2+x+2)2=0 has at least one real root, then range of p is

A
[5,397]
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B
(5,397]
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C
(5,397)
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D
None of these
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Solution

The correct option is B (5,397]
(x2+x+3)2(p3)(x2+x+3)(x2+x+2)+(p4)(x2+x+2)2=0
(x2+x+3)2(x2+x+3)(x2+x+2)
(p4)(x2+x+3)(x2+x+2)+(p4)(x2+x+2)2=0
Factorizing the above equation,
((x2+x+3)(x2+x+2))((x2+x+3)(p4)(x2+x+2))=0
((5p)x2+(5p)x+(112p))=0
For at least one root, (5p)2>4(112p)(5p)
Hence, (5,397]

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