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 Jun 21, 2021

#1**0 **

Given is a quadratic xpression which is greater than equal to 0, thus, D = b^2-4ac <0

(2(4k-1))^2 - 4(15k^2-2k-7)<0

k^2-6k+8<0

(k-2)(k-4)<0

Thus, 2 or, k=3

;)

Technoblade Jun 21, 2021