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The roots of a quadratic equation with rational coefficients

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The roots of a quadratic equation with rational coefficients are p±√q.Write the equation in standard from in terms of p and
Adrien said that if the roof of a quadratic equation are 1\2 and 3\4 ,the equation is 4x^2 -5x +3\2 =0.Olivia said that the equation is 8x^2 -10x +3=0 .Who is correct?Justify your answer.
The roots of a quadratic equation with rational coefficients
 x^2 -2px +p^2-q=0
都对  但第二个方程漂亮些    没有分数
再问: 可以写一下具体过程吗?