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Nature of Roots

Find the valu...

Question

Find the value of $k,$ if $- 4 k^{2} - (- 11)^{2} = 3 k^{2} - 9$ .

\frac{4}{i}

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- 4 i

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4 i

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- \frac{4}{i}

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Solution

The correct options are
C $4 i$
D $- \frac{4}{i}$
$- 4 k^{2} - (- 11)^{2} = 3 k^{2} - 9$
$- 4 k^{2} - 121 = 3 k^{2} - 9$
$- 4 k^{2} - 3 k^{2} = 121 - 9$
$- 7 k^{2} = 112$
$- k^{2} = \frac{112}{7}$
$- k^{2} = 16$
Taking square roots on both the sides we get,
$k = 4 i$
$\Rightarrow k = - \frac{4}{i}$

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