Multiple choice

If one imaginary root of a quadratic equation is $1 - i\sqrt {3}$, then the other root will be:

  1. $\sqrt {3}$
  2. $-\sqrt {3}$
  3. $1$
  4. $1 + i\sqrt {3}$
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D Correct answer
Explanation

For a quadratic equation with real coefficients, imaginary roots always occur in conjugate pairs. The conjugate of 1 - i*sqrt(3) is 1 + i*sqrt(3).

AI explanation

For a quadratic equation with real coefficients, complex or imaginary roots must occur in conjugate pairs. If one root is 1 - i*sqrt(3), its complex conjugate is formed by changing the sign of the imaginary part. Therefore, the other root is 1 + i*sqrt(3).

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