If the equation x2 +2(a+1)x+ 9a-5=0 has only negative roots then 'a' can take which values - Maths - Relations and Functions

Question

If the equation x2 +2(a+1)x+ 9a-5=0 has only negative
roots then 'a' can take which values?

Anuradha Sharma · Accepted Answer

Condition for negative root only is that, D≥0sum of roots<0product of roots>0So here for x2+2a+1x+9a-5=04a+12-4×9a-5≥04a2+4+8a-36a+20≥0a2-7a+6≥0a-6a-1≥0a∈(-∞,1]∪[6,∞) 1second condition, -2a+1<0a+1>0a∈-1,∞ 2and third condition, 9a-5>0a∈59,∞ 3Now intersection of 1, 2, 3 will be the final answer so we get, a∈[6,∞)

If the equation x2 +2(a+1)x+ 9a-5=0 has only negative roots then 'a' can take which values?

If the equation x² +2(a+1)x+ 9a-5=0 has only negative roots then 'a' can take which values?