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Algebra Level 4

If \(m,n\) be roots of quadratic equation \(ax^2+bx+c =0\) ,then roots of the equation \((4a+2b+c)x^2+(4a-b-2c)x+(a-b+c) = 0\) can be expressed as \(\dfrac{m+e}{m+f} , \dfrac{n+g}{n+h}\) . Find the value of the product \(efgh\).

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