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mathdad
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Section 2.6
Question 36Solve the quadratic inequality.
x^4 - 25x^2 + 144 ≤ 0
Can someone get me started?
Question 36Solve the quadratic inequality.
x^4 - 25x^2 + 144 ≤ 0
Can someone get me started?
RTCNTC said:Section 2.6
Question 36Solve the quadratic inequality.
x^4 - 25x^2 + 144 ≤ 0
Can someone get me started?
RTCNTC said:Thank you very much. I am at the AMC about to watch the shark movie 47 Meters Down. I will answer this and the other 3 questions later this evening. Thank you again for your continual help in this website.
A quadratic inequality is an inequality that contains a quadratic expression, which is an algebraic expression with at least one squared term. It typically has the form ax^2 + bx + c, where a, b, and c are constants and x is the variable. An example of a quadratic inequality is x^2 + 4x - 5 < 0.
To solve a quadratic inequality, you first need to rearrange the inequality so that the expression is on one side and 0 is on the other side. Then, you can factor the quadratic expression and find the critical points, which are the points where the expression equals 0. Based on the sign of the expression between these critical points, you can determine the solution to the inequality. Graphing the quadratic expression can also help visualize the solution.
A quadratic equation is an equation that is set equal to 0 and can be solved to find the value(s) of the variable that make the equation true. A quadratic inequality, on the other hand, is an inequality that may have multiple solutions and is solved to find the range of values for the variable that make the inequality true.
To graph a quadratic inequality, you can first graph the corresponding quadratic equation, which will create a parabola. Then, you can use a test point method to determine which region of the graph satisfies the inequality. If the test point satisfies the inequality, then the region containing the test point is part of the solution. If the test point does not satisfy the inequality, then the other region is part of the solution.
Quadratic inequalities are commonly used in physics and engineering to model real-world scenarios, such as projectile motion and optimization problems. They can also be used in economics and finance to analyze profit and cost functions, as well as in computer science for designing algorithms and data structures.