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Question

The equation [1xy]1310210011xy=[0] has

A
rational roots if y=1
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B
irrational roots if y=0
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C
rational roots if y=0
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D
integral roots if y=1
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Solution

The correct option is C rational roots if y=0
Given : [1xy]1310210011xy=[0]
[13+2x1x+y]1xy=[0]
2x2+y2+y+3xxy+1=0

If y=0, 2x2+3x+1=0
Solving this, we get
x=12,1 (rational roots)

If y=1, 2x2+4x+1=0
x=4±84=2±22 (irrational roots)

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