Quadratic inequalities
Solve the inequality over ℝ. Choose the set of all solutions.
Correct answers
To bronze: 0 of 5
Daily streak
To Busy Bee: 0 of 3 days
Today: 0 of 5 exercises
We solve a quadratic inequality using the parabola. We find the roots, the points where the parabola crosses the x-axis. Then we look at where the parabola is above the axis (the expression is positive) and where it is below it (the expression is negative). For (x − 1)(x − 4) < 0 the parabola is below the axis between the roots, so x ∈ (1, 4).
What does this generator do?
At the easy level the left-hand side is in factored form, so you can read off the roots. At the medium level it is expanded with a = 1 or −1. At the hard level there is another number in front of x², and inequalities with a double root or with no real roots also appear.
How to use it
1) Find the roots of the equation ax² + bx + c = 0. 2) Sketch the parabola: for a > 0 it opens upward, for a < 0 downward. 3) For “> 0” you want the part above the x-axis, for “< 0” the part below it. 4) With ≤ and ≥ the roots belong to the solution (square bracket), with < and > they do not.