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How to Find the Inverse of a Function

If 2 + i an...

Question

If $2 + i$ and $\sqrt{5} - 2 i$ are the roots of the equation $(x^{2} + a x + b) (x^{2} + c x + d) = 0$ , where $a, b, c, d$ are real constants, then product of all roots of the equation is

40

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9 \sqrt{5}

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45

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35

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Solution

The correct option is C $45$
$2 - i$ and $\sqrt{5} + 2 i$ are other roots.
So, Product is $(2 + i) (2 - i) (\sqrt{5} + 2 i) (\sqrt{5} - 2 i)$
$= 5 \times 9 = 45$

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