$3 - 2i$ and $3 + 2i$ are roots of the quadratic equation:
- $x^{2} + 6x + 13 = 0$
- $x^{2} - 6x + 13 = 0$
- $x^{2} - 6x - 13 = 0$
- $x^{2} + 6x + 7 = 0$
- $x^{2} + 6x - 4 = 0$
Reveal answer
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B
Correct answer
Explanation
If roots are 3 +/- 2i, the sum is 6 and the product is 3^2 + 2^2 = 13. The equation is x^2 - (sum)x + (product) = 0, which is x^2 - 6x + 13 = 0.
AI explanation
Use the sum and product of roots to form the quadratic equation, where the sum of the roots is (3 - 2i) + (3 + 2i) = 6 and the product is (3 - 2i)(3 + 2i). The product simplifies using the difference of squares identity to 9 - (-4) = 13. Substituting these into the standard form x^2 - (sum)x + (product) = 0 gives x^2 - 6x + 13 = 0.