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

Answer 1

#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#
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Answer 2

To solve the equation (x^2 + 5x + 4 \geq 0), first factor the quadratic expression: ((x + 1)(x + 4) \geq 0). Then, determine the intervals where the expression is greater than or equal to zero using the signs of the factors: (-4 \leq x \leq -1) and (x \geq -4). So, the solution is (x \in [-4, -1] \cup [-1, \infty)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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