# Square Inequality

In square inequality we have two options:

1. Given the square inequality:

$$ax^2+bx+c>0, a> 0$$

And the roots of the quadratic equation are

$$x_1

In this case, we find the inequality solution with Delta’s calculation:

$$\Delta=b^2-4ac$$

Now, there are 3 options:

1.1. When

$$\Delta>0$$

The solution of the inequality is

$$xx_2$$

1.2. When

$$\Delta=0$$

The solution is

$$x\neq -\frac{b}{2a}$$

1.3. When

$$\Delta<0$$

The solution of the inequality is all x.

2. Given the square inequality:

$$ax^2+bx+c<0, a> 0$$

And the roots of the quadratic equation are

$$x_1

Here, too, we find the solution of inequality with Delta’s calculation:

$$\Delta=b^2-4ac$$

Again, there are 3 options:

1.1. When

$$\Delta>0$$

The solution of the inequality is

$$x_1

1.2. When

$$\Delta=0$$

There is no real solution to the equation.

1.3. when

$$\Delta<0$$

There is no real solution to the equation.

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