Find the value of g, given that $8 x^{2} + 2 x + g = 0$ and $2 x^{2} + g x + 1 = 0$ have a common root.

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None of the above

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Solution

The correct option is D None of the above
To find the common root, equate the two equations

$2 x^{2} + g x + 1 = 8 x^{2} + 2 x + g$

$- 6 x^{2} + x (g - 2) + (1 - g) = 0$

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, according to the question also, there is a single root which is common, hence D=0)

We will get it as : $g^{2} - 28 g + 28 = 0$

Check with answer options at this stage

None of the values of g is being satisfied.

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