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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