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$I f x^{2} + p x + q = 0 h a s r o o t s 2 i + 3, 2 i - 3 t h e n t h e d i s c r i \min a n t o f t h e e q u a t i o n i s$

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a

36

b

-36

c

-16

d

32

answer is A.

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Detailed Solution

$\begin{array}{l} L e t α = 2 i + 3, β = 2 i - 3 a r e r o o t s o f x^{2} + p x + q = 0 \\ α + β = - p \Rightarrow p = - (2 i + 3 + 2 i - 3) = - 4 i \\ α β = q \Rightarrow q = (2 i + 3) (2 i - 3) = - 13 \\ D i s c r i \min a n t = p^{2} - 4 q \\ = {(- 4 i)}^{2} - 4 (- 13) \\ = - 16 + 52 \\ = 36 \end{array}$

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If x2+px+q=0 has roots 2i+3, 2i−3 then the discriminant of the equation is