Mister Exam
t^2+4*t<0 inequation
The solution
Detail solution
Given the inequality:
$$t^{2} + 4 t < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$t^{2} + 4 t = 0$$
Solve:
$$x_{1} = -4$$
$$x_{2} = 0$$
$$x_{1} = -4$$
$$x_{2} = 0$$
This roots
$$x_{1} = -4$$
$$x_{2} = 0$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-4 + - \frac{1}{10}$$
=
$$-4.1$$
substitute to the expression
$$t^{2} + 4 t < 0$$
$$t^{2} + 4 t < 0$$
Then
$$x < -4$$
no execute
one of the solutions of our inequality is:
$$x > -4 \wedge x < 0$$
$$t^{2} + 4 t < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$t^{2} + 4 t = 0$$
Solve:
$$x_{1} = -4$$
$$x_{2} = 0$$
$$x_{1} = -4$$
$$x_{2} = 0$$
This roots
$$x_{1} = -4$$
$$x_{2} = 0$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-4 + - \frac{1}{10}$$
=
$$-4.1$$
substitute to the expression
$$t^{2} + 4 t < 0$$
$$t^{2} + 4 t < 0$$
2
t + 4*t < 0
Then
$$x < -4$$
no execute
one of the solutions of our inequality is:
$$x > -4 \wedge x < 0$$
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