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Q.

For K > 0, if $K \sqrt{- 1}$ is a root of the equation $x^{4} + 6 x^{3} - 16 x^{2} + 24 x - 80 = 0$ then K²=____

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a

2

b

6

c

3

d

4

answer is C.

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Detailed Solution

$f (k i) = 0 \Rightarrow (k^{4} + 16 k^{2} - 80) + i (24 k - 6 k^{3}) = 0 = 0 + i (0)$

Comparing Img. Part $\Rightarrow k = 4$

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For K > 0, if K−1 is a root of the equation x4+6x3−16x2+24x−80=0 then K2=____