Question

find the vales of k for which the equation x²+5kx+16=0 has no real roots

Answer 1

x2+5kx+16=0
a=1
b=5k
c=16
b2-4ac<0
25k2-4x1x16<0
25k2-64<0
(5k+8)(5k-8)<0
5k+8<0
k<-8/5
k<-1.6
5k-8<0
k<1.6
Value of k=(-1.7,-1.8,-1.9...............infinity)