Multiple choice

If one root of the quadratic equation, ix2 - 2(i + l) x + (2 - i) = 0 is 2 - i, then the other root is:

    • i

  2. i

  3. 2 + i

  4. 2 - i
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A Correct answer
Explanation

Using the sum of roots, the sum is 2(i + 1)/i = 2 - 2i. Subtracting the known root 2 - i gives the other root as -i.

AI explanation

For the quadratic equation ix2 - 2(i + 1)x + (2 - i) = 0, we use the relationship between roots and coefficients, where the sum of the roots equals -b/a. Let the roots be 2 - i and r, giving the sum (2 - i) + r = 2(i + 1)/i. Simplifying the right side, 2(i + 1)/i = 2(1 - i), so the equation is (2 - i) + r = 2 - 2i. Solving for r, we get r = 2 - 2i - 2 + i, which simplifies to -i. Therefore, the other root is -i.

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