(D) Given that $2+4i$ is one of the roots of the quadratic equation $x^2+bx+c=0$ where $b, c \in R$. Since the coefficients are real,the complex roots

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(D) Given that $2+4i$ is one of the roots of the quadratic equation $x^2+bx+c=0$ where $b, c \in R$. Since the coefficients are real,the complex roots must occur in conjugate pairs. Therefore,the other root is $2-4i$. Sum of roots $= -b = (2+4i) + (2-4i) = 4$. Thus,$b = -4$. Product of roots $= c = (2+4i)(2-4i) = 2^2 - (4i)^2 = 4 + 16 = 20$. Thus,$c = 20$. Therefore,$(b, c) = (-4, 20)$. Hence,option $(d)$ is correct.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Solution of quadratic equations and Nature of roots

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If $2+4i$ is one of the roots of $x^2+bx+c=0$ with $b, c \in R$,then $(b, c) =$

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$(4, -20)$
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$(4, 20)$
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$(-4, -20)$
D
$(-4, 20)$

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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