**General Formula**

for Solutions of Quadratic Inequalities

The table below represents two general formulas that express the solution of a quadratic inequality of a parabola that opens upwards (ie a > 0) whose roots are r_{1} and r_{2}.

**The Greater Than Inequality**

0 > ax² + bx + c

**Solution:** {x| r_{1} < X < r_{2}}

**The Less Than Inequality**

0 < ax² + bx + c

**Solution:** {x| x < r_{1} or x > r_{2}}

We can reproduce these general formula for inequalities that include the quadratic itself (ie ≥ and ≤).

**The Greater Than Inequality**

0 ≥ ax² + bx + c

**Solution:** {x| r_{1} ≤ X ≤ r_{2}}

**The Less Than Inequality**

0 ≤ ax² + bx + c

**Solution:** {x| x ≤ r_{1} or x ≥ r_{2}}

Warning about imaginary solutions:

Although the solution of a quadratic equation could be imaginary. The solution of a quadratic inequality cannot include imaginary numbers -- this is because imaginary numbers cannot be ordered.