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Question

The roots of the equation 2x4+x311x2+x+2=0 is/are

A
12
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B
14
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C
352
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D
5+32
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Solution

The correct option is C 352
Given equation
2x4+x311x2+x+2=0
Dividing the given equation by x2, as x=0 is not the root of the equation.
2x2+x11+1x+2x2=02(x2+1x2)+(x+1x)11=02((x+1x)22)+(x+1x)11=02(x+1x)2+(x+1x)15=0

Assuming x+1x=t
2t2+t15=0
(t+3)(2t5)=0t=3 or 52
Now,
x+1x=3
x2+3x+1=0x=3±942=3±52

x+1x=52
2x25x+2=0(x2)(2x1)=0x=2,12

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