Multiple choice

If $(3 + i )$ is a root of the equation $ x^{2}+ax+b=0 $, where $a$ and $b$ are rationals, then $a$ is equal to

  1. $3$
  2. $-3$
  3. $6$
  4. $-6$
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D Correct answer
Explanation

If coefficients are rational, complex roots occur in conjugate pairs. Roots are 3+i and 3-i. Sum of roots = -a = (3+i)+(3-i) = 6, so a = -6.

AI explanation

Since the coefficients of x^2 + ax + b = 0 are rational, the complex conjugate 3 - i must also be a root. The sum of the roots is (3 + i) + (3 - i) = 6. By Vieta's formulas, the sum of the roots equals -a, so -a = 6. Therefore, a is equal to -6.

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