The equation $x^{2} + k^{2} = 3 - k + 2 k x$ has normal no real solutions
Find the possible values of $k$

k > 3

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k \geq 3

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k \leq 3

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k < 3

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Solution

The correct option is A $k > 3$
Given the equation is $x^{2} + k^{2} = 3 - k + 2 k x$
or, $x^{2} - 2 k x + k^{2} + k - 3 = 0$
This equation will've no real solution if the discriminant of the equation is $< 0$ .
Then,
$(- 2 k)^{2} - 4 (k^{2} + k - 3) < 0$
or, $k^{2} - (k^{2} + k - 3) < 0$
or, $3 - k < 0$
or, $k > 3$ .

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