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Question

The linear factor(s) of the equation x2+4xy+4y2+3x+6y4=0 is/are

A
x+2y+1=0
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B
x+2y1=0
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C
x+2y+4=0
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D
x+2y4=0
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Solution

The correct option is C x+2y+4=0
x2+4xy+4y2+3x+6y4=0
Writing equation in terms of y, we get
4y2+(4x+6)y+(x2+3x4)=0
Now, using quadratic formula, we have
y=(4x+6)±(4x+6)244(x2+3x4)24
y=(4x+6)±1024
y=(2x+3)±54y=x+12 or y=x42x+2y1=0 or x+2y+4=0



Alternate Solution:
x2+4xy+4y2+3x+6y4=0(x2+4xy+4y2)+(3x+6y)4=0(x+2y)2+3(x+2y)4=0((x+2y)+4)((x+2y)1)=0x+2y+4=0 or x+2y1=0



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