x = 1/4 and x =-1 are roots so, (x-1/4)(x+1) are factors of quadratic equation.
(x-1/4)(x+1) = 0
(4x - 1)(x+1) = 0
4x2 - x + 4x -1 =0
4x2 + 3x -1 =0
Hence the required quadratic equation is 4x2 + 3x -1 =0
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