Which condition on \\(k\\) is necessary for the equation \\(5x^2+2kx+2=0\\) to have real roots?

Correct answer: or \\(k\\ge \\sqrt{10}\\)

For the quadratic equation, \\(a=5\\), \\(b=2k\\), and \\(c=2\\). Real roots require the discriminant \\(D=b^2-4ac\\ge0\\). Thus, \\(D=(2k)^2-4(5)(2)=4(k^2-10)\\ge0\\), giving \\(k^2\\ge10\\), or \\(k\\le-\\sqrt{10}\\) or \\(k\\ge\\sqrt{10}\\). In option B, \\(D<0\\), so the roots are not real. Exam tip: For real roots, use \\(D\\ge0\\); equality represents two equal real roots.