+0  
 
0
105
6
avatar

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.

 Apr 14, 2022
 #1
avatar+578 
+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

 

smileysmileysmiley

 

 

 

 

Used as reference:

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

 Apr 14, 2022
 #6
avatar+33145 
+1

Note that the question asks for real numbers - it doesn't restrict the solution to integers.

Alan  Apr 15, 2022
 #2
avatar+114 
-2

Mhmmmmm

 Apr 14, 2022
 #3
avatar+578 
+1

What happened?

Vinculum  Apr 14, 2022
 #4
avatar+114 
-2

i need help

Kakashi  Apr 14, 2022
 #5
avatar+114 
-5

Im trying to get on a high level for a certain thing

Kakashi  Apr 14, 2022

17 Online Users