If one root of quadratic equation $- x^{2} + a x + b = 0$ , where a, b, c are real, is -1+2i, then the value of a+b is .

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-3

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-7

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Solution

The correct option is D -7
$I f α = - 1 + 2 i, t h e n β = - 1 - 2 i \Rightarrow α + β = - 2, a n d \Rightarrow α β = 1 + 4 = 5 ∴ r e q u i r e d e q u a t i o n w i l l b e : x^{2} + 2 x + 5 = 0 \Rightarrow - x^{2} - 2 x - 5 = 0 O n c o m p a r i n g, a = - 2, b = - 5 ∴ a + b = - 7$

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