Question

For which of k does the function have no root ? AND WHY ?
F(x) = kx^2 -kx-5

Answer 1

disc of kx^2-kx-5 is \[b^2-4ac=\left( -k \right)^2-4k(-5)=k^2+20k\] it has no root if \[k^2+20k<0\]
add 100 to both sides
\[k^2+20k+100<100,\left( k+10 \right)^2<10^2,\left| k+10 \right|<10\]
-10<k+10<10
-20<k<0
if the value of k is between -20 and 0 then it has no root.