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Algebra Level 4

\[(x-t_1)(x-t_3)+k(x-t_2)(x-t_4)=0\]

Find the values of \(k\) for which the above equation has real roots, if provided that \(t_1<t_2<t_3<t_4\).

No such value of \(k\) exists \[k \in (t_1,t_2) \cup (t_3,t_4)\] \[k \in (t_1,t_3) \cup (t_2,t_4)\] All real numbers

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Excel in math and science

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by Sandeep Bhardwaj

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