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Part BConsider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero? A. The other zero must be rational. B. The other zero must be irrational. C. The other zero can be either rational or irrational. D. The other zero must be non-real.

Question

Part BConsider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero? A. The other zero must be rational. B. The other zero must be irrational. C. The other zero can be either rational or irrational. D. The other zero must be non-real.

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Solution

The correct answer is B. The other zero must be irrational. This is due to the Conjugate Root Theorem, which states that if a polynomial has rational coefficients and one root is a non-real complex number or an irrational number, then its conjugate must also be a root. In this case, if one root of a quadratic equation is irrational, then the other root must also be irrational.

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