Solve the equation #x^2+5x+4 ge 0 #?

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Answer 1 · 2017-11-30T12:44:58

#x le -4# or #x ge -1#

We have:

# x^2+5x+4 ge 0 #

We first solve the equation:

# x^2+5x+4 = 0 => (x+4)(x+1)=0#
# => x=-1, -4 #

Ther using appropriate software or a graphical calculator we examine the graph:
graph{ y=x^2+5x+4 [-10, 10, -5, 5]}

And if we add shading we seek the range in which the curve lies above the #x#-axis.
graph{ (y-x^2-5x-4)(sqrt(y))^2 <= 0 [-10, 10, -5, 5]}

and we see from the graph that:

# { (x le -4),(-4 lt x lt -1), (x ge -1) :} => { (x^2+5x+4 ge 0),(x^2+5x+4 lt 0), (x^2+5x+4 ge 0) :} #

Thus we have:

#x le -4# or #x ge -1#