Question

Find the value of $k$ so that equation $(k+4)x^2+(k+1)(x+1)=0$

Answer 1

$(k+4)x^2+(k+1)x+(k+1)=0$

$△=(k+1{)}^2-(k+4\left)\right(k+1)$

$=(k+1)(-3)$

but $△\ge 0$,

$△k+1\le 0$

$△k\le -1$

$k\le (-\infty ,-1]$