For which values of $k$ is $x^{2} + k x + 4 > 0$ for every real $x$ ?

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For which values of $k$ is $x^{2} - 2 k x + k + 2 > 0$ for every real $x$ ?
For which values of $k$ does $x^{2} - 6 x + k = 0$ have two distinct positive real roots?
For which values of $k$ does $x^{2} + (k - 2) x + k = 0$ have real roots?
For which values of $k$ does the line $y = 2 x + k$ meet the circle $x^{2} + y^{2} = 5$ at two distinct points?
For which values of $k$ (with $k \neq = 0$ ) does $k x^{2} + 4 x + k = 0$ have no real roots?