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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<x_2

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

x<x_1 \text{ or } x>x_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<x_2

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<x<x_2

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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