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  4. The midpoint of the interval in which x2-2(√-x)2-3< 0 is satisfied, is

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Q. The midpoint of the interval in which $x^2-2(\sqrt{-x})^2-3< 0$ is satisfied, is

Complex Numbers and Quadratic Equations

Solution:

$ x^2-2(\sqrt{-x})^2-3<0$ is valid only if $x<0$
Then $x ^2+2 x -3<0 \Rightarrow( x +3)( x -1)<0 \Rightarrow -3< x <1$
Since $x<0$ hence $x \in(-3,0)$
The midpoint of the interval is $\frac{-3}{2}$