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Question

The value of P for which the equation (P33P2+2P)x2+(P3P)x+P3+3P2+2P=0 has exactly one root at infinity is

A
1
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B
1
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C
0
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D
2
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Solution

The correct option is D 2
If ax2+bx+c=0 has exactly one root at infinity, then it implies that a=0 and b0.
Given (P33P2+2P)x2+(P3P)x+P3+3P2+2P=0
Comparing both, we get
P33P2+2P=0
P(P23P+2)=0
P(P22PP+2)=0
P(P1)(P2)=0
P=0,1,2(i)

Also,
P3P0
P(P1)(P+1)0
P0,±1(ii)

From (i) and (ii), we get
P=2



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