A quadratic equation with real coefficients whose one root is $3-2 i$ is
- $x^2 - 3x + 2 = 0$
- $x^2 - 6x + 13 = 0$
- $x^2 - 2x + 3 = 0$
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None of these
Reveal answer
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B
Correct answer
Explanation
If a quadratic equation with real coefficients has a complex root 3 - 2i, it must also have the conjugate root 3 + 2i. The equation is (x - (3 - 2i))(x - (3 + 2i)) = 0, which simplifies to (x - 3)^2 - (2i)^2 = x^2 - 6x + 9 + 4 = x^2 - 6x + 13 = 0.
AI explanation
Since the quadratic equation has real coefficients, the complex roots must occur in conjugate pairs. With one root given as 3 - 2i, the other root must be 3 + 2i. We find the sum of the roots to be 6 and the product of the roots to be 9 + 4 = 13. Using the standard form x^2 - (sum)x + (product) = 0, the equation is x^2 - 6x + 13 = 0.