Multiple choice

If $2-i$ is one root of the equation $ax^2 - bx + c = 0$, and $a,b,c$ are rational numbers, then the other root is

  1. $- i - 2$
  2. $i - 2$
  3. $2 + i$
  4. $2i + i$
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C Correct answer
Explanation

For a polynomial equation with rational coefficients, complex roots must occur in conjugate pairs. If 2 - i is a root, its conjugate 2 + i must also be a root.

AI explanation

Since the coefficients a, b, and c of the quadratic equation are rational numbers, any complex root must occur in conjugate pairs. The complex conjugate of the root 2 minus i is obtained by reversing the sign of the imaginary part. Therefore, the other root is 2 plus i.

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