Quadratic inequality-interval notation

In summary, to solve the inequality 2x^2<-x+10 and put it into interval notation, you would first solve the corresponding equation 2x^2+x-10=0. The solutions of the equation become the boundaries of sets of numbers that are solutions to the inequality. By testing values less than the smaller solution, between the two solutions, and greater than the larger solution, you can determine the intervals that satisfy the inequality and write it in interval notation.
  • #1
Torshi
118
0
quadratic inequality--interval notation..

Homework Statement



2x^2<-x+10
Solve inequality and put into interval notation

Homework Equations



interval notation

The Attempt at a Solution


I don't even know where to start. I set it equal to zero -2x^2-x+10=0
 
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  • #2


It's fine to start by solving the corresponding equation. The solutions of the equation become "boundaries," if you will, of sets of numbers that are solutions to the inequality. Suppose there are two solutions, a & b, with a < b. Then you would have 3 potential range of numbers to test.

Pick a value less than a and test into the original inequality. If the result is a true statement, then x < a would be in the solution set.

Then pick a number between a and b and test. If it works, then a < x < b is in the solution set.

Finally, pick a number in greater than b. If it works, then x > b is in the solution set.
 

FAQ: Quadratic inequality-interval notation

What is a quadratic inequality?

A quadratic inequality is an inequality that contains a quadratic function, with the highest degree of the variable being 2. It can be written in the form of ax^2 + bx + c < 0, where a, b, and c are constants and x is the variable.

What is interval notation?

Interval notation is a way of representing the solution set of an inequality using a combination of parentheses and brackets. For example, (a, b) would represent all real numbers between a and b, including a and b, while [a, b] would represent all real numbers between a and b, including a but not b.

How do you graph a quadratic inequality?

To graph a quadratic inequality, first plot the corresponding quadratic function. Then, determine whether the inequality is less than or greater than, and shade the appropriate region on the graph. If the inequality includes an equal sign, use a solid line for the boundary. If the inequality does not include an equal sign, use a dashed line for the boundary.

What is the solution set of a quadratic inequality?

The solution set of a quadratic inequality is the set of all real numbers that make the inequality true. It can be represented using interval notation or set-builder notation.

What are some real-world applications of quadratic inequalities?

Quadratic inequalities can be used to model and solve real-world problems, such as determining the maximum or minimum value of a function, optimizing a business's profits, or finding the range of possible values for a given situation.

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