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True roots are the actual solutions to an equation, meaning they satisfy the equation when substituted back in. False roots, on the other hand, may arise from the algebraic manipulation of an equation but do not satisfy it when checked. For example, if an equation is manipulated incorrectly, it might yield a false root that does not hold true upon verification. In the context of polynomial equations, true roots correspond to the x-values where the polynomial crosses the x-axis, while false roots do not have this geometric interpretation.

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2mo ago

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