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(B) The given quadratic equation is $x^2 + 2kx + 4 = 0$.For a quadratic equation $ax^2 + bx + c = 0$,the nature of roots is determined by the discrimi

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Real and unequal

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(B) The given quadratic equation is $x^2 + 2kx + 4 = 0$.For a quadratic equation $ax^2 + bx + c = 0$,the nature of roots is determined by the discriminant $D = b^2 - 4ac$.Here,$a = 1$,$b = 2k$,and $c = 4$.$D = (2k)^2 - 4(1)(4) = 4k^2 - 16$.For the roots to be real and unequal,we must have $D > 0$.$4k^2 - 16 > 0$ $\Rightarrow 4(k^2 - 4) > 0$ $\Rightarrow k^2 > 4$.This inequality holds when $k \in (-\infty, -2) \cup (2, \infty)$.Since the given condition is $k \in (-\infty, -2) \cup (2, \infty)$,the discriminant $D$ is always greater than $0$.Therefore,the roots are real and unequal.

If $k \in (-\infty, -2) \cup (2, \infty)$,then the roots of the equation $x^2 + 2kx + 4 = 0$ are

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