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Consider the quadratic equation ax^2+bc+c=0, where a, b, c are rational numbers and the quadratic has two distinct zeros. If one zero is rational, which of the following is true…

Consider the quadratic equation ax^2+bc+c=0, where a, b, c are rational numbers and the quadratic has two distinct zeros. If one zero is rational, which of the following is true…
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Consider the quadratic equation ax^2+bc+c=0, where a, b, c are rational numbers and the quadratic has two distinct zeros. If one zero is rational, which of the following is true of the other zero?

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User Gabriel Petrovay
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With rational coefficients (a, b and c), if one zero is rational, that means the discriminant is rational.  We can conclude that the other is also rational.
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User Sjmh
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