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Question

Find the value of g, given that 8x2+2x+g=0 and 2x2+gx+1=0 have a common root?

A
1
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B
2
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C
3
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D
a and b
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E
None of the above
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Solution

The correct option is E None of the above

OPTION E

To find the common root, equate the two equations

2x2+gx+1=8x2+2x+g

-6x2+x(g-2)+(1-g)=0

Now find the discriminant of this equation and equate that to 0(D=0 means that the roots are equal and there exists a single root, acording to the question also, there is a single root which is common, hence D=0)

we will get it as : g2 - 28g +28 = 0

Check with answer options at this stage

None of the values of x is being satisfied, hence option e.


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