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Question

lf the equations 2x27x+1=0 and ax2+bx+2=0 have a common root and a,b are rational, then

A
a=2,b=7
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B
a=72,b=1
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C
a=4,b=14
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D
a=4,b=1
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Solution

The correct option is C a=4,b=14
We have 2x27x+1=0x=7±724×22×2=7±414=irrational
And we know that irrational roots of a quadratic occur in pair
Hence both the roots of given quadratics have to be common
2a=7b=12
a=4,b=14

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