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Question

If the equations x211x+a=0 & x214x+2a=0 have a common root, then value of a equals

A
0,24
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B
0,1
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C
3,2
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D
None of these
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Solution

The correct option is A 0,24
x214x+2a=0
x211x+a=0
Subtracting second equation from first, we get
x(14+11)+a=0
x(3)=a
x=a3 which is the common root
Substituting, we get
a2911a3+a=0
a(a9113+1)=0
Hence,
a=0 or a983=0
a=24.

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