Question

The integer k for which the inequality x^2-2(4k-1)x+15k^2-2k-7>0 is valid for any x is

Answer 1

The inequality will be greater than zero if D is less than zero

4(4k-1)2 – 4(15k2 – 2k – 7) less than zero

Simplifying this we get

K2-6k+8 less than zero

(k-4)(k-2) less than zero

So we know that

K lies in (2, 4)