Question

Solve this math!! Only for intelligent people

Answer 1

Final Answer : 2<k<4

Steps:
1)
${x}^{2} - 2(4k - 1)x + 15 {k}^{2} - 2k - 7 > 0$
This quadratic equation is always positive,
=> Graph is upward parabola which doesn't cut x - axis
=> D < 0
=>
${(2(4k - 1))}^{2} - 4 \times \\ (15 {k}^{2} - 2k - 7) < 0 \\ = > 64 {k}^{2} - 32k + 4 - 60 {k}^{2} + 8k + 28 < 0 \\ = > 4 {k}^{2} - 24k + 32 < 0 \\ = > {k}^{2} - 6k + 8 < 0 \\ = > (k - 4)(k - 2) < 0 \\ = > 2 < k < 4$