the integer k for which the inequality x^2 - 2(4k-1)x +15m^2 - 23k - 7 0 is valid - Maths - Complex Numbers and Quadratic Equations

Question

the integer k for which the inequality x^2 - 2(4k-1)x +15m^2 -
23k - 7 > 0 is valid for any x is:

Ishwarmani · Accepted Answer

Dear Student, Please find below the solution to the asked query: x2-24k-1x+15k2-23k-7>0This is true if a>0 and D<0 Here, a=1>0So, D<0-24k-12-415k2-23k-7<0⇒416k2-8k+1-60k2+92k+28<0⇒64k2-32k+4-60k2+92k+28<0⇒4k2+60k+32<0⇒k2+15k+8<0⇒k∈-15-1932,-15+1932 As, for k2+15k+8=0,k=-15±225-322=-15±1932So, integral values of k are -14,-13,-12,-11, ,-1 Hope this information will clear your doubts about the topic Regards

the integer k for which the inequality x^2 - 2(4k-1)x +15m^2 - 23k - 7 > 0 is valid for any x is: