Solve the inequalities. 2 x^2+3 x+3>0

Name: Problem 64, Chapter 7: Intermediate Algebra
Uploaded: 2020-07-20T07:03:16-08:00
Duration: 2 min 23 s
Channel: Ankit Gupta
Description: Solve the inequalities. 2 x^2+3 x+3>0

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Key Concepts

Discriminant Analysis

The discriminant, given by b² - 4ac, helps determine the nature and number of roots of a quadratic equation. When solving quadratic inequalities, a negative discriminant implies there are no real roots, meaning the quadratic expression does not cross the x-axis. Consequently, its sign is determined solely by the leading coefficient.

Quadratic Inequalities

Quadratic inequalities involve expressions of the form ax² + bx + c which are compared to zero (or another expression) using inequality symbols. Solving them requires determining the intervals where the quadratic expression takes positive or negative values, often by finding the roots and testing intervals between and outside the roots.

Leading Coefficient

The sign of the leading coefficient a in the quadratic expression ax² + bx + c plays a crucial role in determining the graph's direction. If a is positive, the parabola opens upward, and if a is negative, it opens downward. This property allows us to conclude whether the expression is always positive or negative when no real roots exist.

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