If 2 i radic 3 where i radic 1 is a root of the equation x2 ax b 0 then what is ...........

Mathematics (NDA) Complex Numbers

If 2 - i √3 where i = √-1 is a root of the equation x² + ax+ b = 0, then what is the value of(a+ b)?

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2023 NDA -1 Math

-11

-3

- Given a quadratic equation: \(x^2 + ax + b = 0\).

- One root is \(2 - i\sqrt{3}\).

- For real coefficients, complex roots appear in conjugate pairs, so the other root is \(2 + i\sqrt{3}\).

- The sum of roots (using Vieta's formulas) is: \((2 - i\sqrt{3}) + (2 + i\sqrt{3}) = 4\).

- Vieta's formula gives sum of roots as \(-a\), so \(a = -4\).

- The product of roots is \((2 - i\sqrt{3})(2 + i\sqrt{3}) = 4 + 3 = 7\).

- Vieta's formula gives product of roots as \(b\), so \(b = 7\).

- Therefore, \(a + b = -4 + 7 = 3\).

Option 4: 3 is the correct answer.

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