A quadratic inequality is an inequality that can be written in the form of a quadratic equation. The solution set of a quadratic equation is the set of all values of x that make the equation true. For example, the equation x^2 + 4x + 3 = 0 has the solution set {-1, -3}. This means that if x is any real number except -1 or -3, the equation is not true.
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What are the solutions to a quadratic equation if the discriminant is positive?
A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are real numbers and x is an unknown. The solutions to a quadratic equation if the discriminant is positive are given by the quadratic formula: x = -b +/- sqrt(b^2 - 4ac)/2a. In other words, the solutions are the roots of the equation, which can be found by using the quadratic formula. If the discriminant is positive, then the equation has two real roots. If the discriminant is negative, then the equation has no real roots. If the discriminant is zero, then the equation has one real root.
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Frequently Asked Questions
How do you graph a quadratic inequality?
Start by graphing the parabola. Then fill in the region either above or below it, depending on the inequality.
What are the general forms of the quadratic inequalities?
There are two general forms of the quadratic inequalities: ax2 + bx+c < 0 and ax2 + bx+c ≤ 0.
What is the relationship between linear inequalities and quadratic inequalities?
Both linear and quadratic inequalities share the same general relationship: greater than inequalities are the region above the equation's graph and less than inequalities are made up by the region underneath the graph of the equation.
What is quadratic graphing and solving?
Quadratic graphing and solving is a process used to solve quadratic inequalities. In these inequalities, two squares are involved (the domain and the range), with one of the squares containing a variable that can take on different values. To solve these inequalities, you need to know how to graph points and shade a graph.
Which region of the graph represents the quadratic inequality?
The yellow region represents the graph of the quadratic inequality.
Sources
- https://brainly.com/question/12907355
- https://www.chegg.com/homework-help/questions-and-answers/solution-set-quadratic-inequality-ax-2-bx-c-0-1-q106132973
- https://www.cuemath.com/algebra/discriminant/
- https://www.wikihow.com/Solve-Quadratic-Inequalities
- https://9to5science.com/solution-set-of-a-quadratic-inequality
- https://brainly.com/question/13585562
- https://www.geeksforgeeks.org/how-to-find-the-discriminant-of-a-quadratic-equation/
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