# 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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