![image](https://tex.z-dn.net/?f=3x%5E2%2B2kx%2B7%3D0%5C%5CD%3E0%5C%5CD%3D%282k%29%5E2-4%2A3%2A7%3D4k%5E2-84%5C%5C4k%5E2-84%3E0%7C%3A4%5C%5Ck%5E2-21%3E0%5C%5C%28k-+%5Csqrt%7B21%7D%29%28k%2B++%5Csqrt%7B21%7D%29%3E0%5C%5C%5C%5Ck%5Cin%28-%5Cinfty%3B-++%5Csqrt%7B21%7D%29+%5Ccup%28++%5Csqrt%7B21%7D%3B%2B%5Cinfty%29+)
0\\D=(2k)^2-4*3*7=4k^2-84\\4k^2-84>0|:4\\k^2-21>0\\(k- \sqrt{21})(k+ \sqrt{21})>0\\\\k\in(-\infty;- \sqrt{21}) \cup( \sqrt{21};+\infty) " alt="3x^2+2kx+7=0\\D>0\\D=(2k)^2-4*3*7=4k^2-84\\4k^2-84>0|:4\\k^2-21>0\\(k- \sqrt{21})(k+ \sqrt{21})>0\\\\k\in(-\infty;- \sqrt{21}) \cup( \sqrt{21};+\infty) " align="absmiddle" class="latex-formula">