The equation $x^2 + nx + m = 0,$ where $n, m \in I$ can not have:
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integral roots
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non-integral rational roots
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irrational roots
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complex roots
Reveal answer
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B
Correct answer
Explanation
For x^2 + nx + m = 0 with integer coefficients, if the roots are rational, they must be integers (by the Rational Root Theorem). Thus, it cannot have non-integral rational roots.
AI explanation
By the rational root theorem, if a monic polynomial like x^2 + nx + m = 0 has integer coefficients, any rational root must necessarily be an integer. Because n and m are integers, the coefficients are integers, eliminating the possibility of a fraction like 1/2 being a root while still having rational solutions. Therefore, while the equation can have integral, irrational, or complex roots, it cannot have non-integral rational roots.