Find all real numbers K such that the inequality x^2 - 2(4K-1)x + 15K^2 - 2K- 7> 0 holds for all real x.

Guest Apr 14, 2022

#1**+2 **

*The inequality will be greater than zero*

* if D is less than zero.*

*D<0*

*4(4k−1)2−4.1.(15k2−2k−7)<0*

*Simplifying this we get*

*K2−6k+8<0*

*(k−4)(k−2)<0*

*∴k lies in (2,4)*

*In this interval, only one integer is present i.e 3*

**∴k=3**

*-Vinculum*

*Used as reference:*

*https://www.toppr.com/ask/en-us/question/the-integer-k-for-which-the-inequality-x2-24k-1x-15k2/*

Vinculum Apr 14, 2022