Discriminate carefully

Algebra Level 4

The following equation has two solutions \(x_1\) and \(x_2:\) \[x^2 + bx + c = 0,\] where \(b\) and \(c\) are real numbers. Someone claims,

"In order for both \(x_1\) and \(x_2\) to be rational numbers, it is necessary and sufficient that the discriminant \(D = b^2 - 4c\) is the square of a rational number."

It this true or false?

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