step 1 we have to solve this given quadratic equation that is x squared plus 4x plus 5 that is equal to

Solve X^2-5 x+4 ≤0

Name: Problem 540, Chapter 18: Algebra and Trigonometry
Uploaded: 2020-07-11T00:15:03-08:00
Duration: 2 min 1 s
Channel: Ankit Gupta
Description: Solve X^2-5 x+4 ≤0

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Key Concepts

Critical Points

Critical points are the values of the variable where the quadratic expression equals zero. These points are crucial because they divide the number line into distinct intervals, which can then be analyzed individually to determine where the inequality holds.

Sign Chart Analysis

Sign chart analysis is a method used to determine the sign (positive or negative) of a quadratic expression within and outside the intervals defined by its critical points. This technique helps in identifying the regions that satisfy the inequality by testing representative values in each interval.

Quadratic Equations

A quadratic equation is an expression of the form ax² + bx + c = 0, where a, b, and c are constants. Understanding quadratic equations is important because they help determine the roots or critical points, which serve as boundary markers in analyses involving quadratics.

Quadratic Inequalities

A quadratic inequality is similar to a quadratic equation but involves an inequality sign (such as <, ?, >, or ?). These inequalities require determining the intervals on the real number line where the quadratic expression satisfies the inequality condition.

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