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Question

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

A
1
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B
2
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C
0
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D
2
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Solution

The correct option is A 1
If ax2+bx+c=0 has both the roots at infinity, then it implies that a=0,b=0 and c0.
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,
P3P=0
P(P1)(P+1)=0
P=0,±1(ii)

Also,
P3+3P2+2P0
P(P2+3P+2)=0
P(P2+2P+P+2)0
P(P+1)(P+2)0
P0,1,2(iii)
From (i),(ii),(iii), we get
P=1

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