Solution assignment 06 Quadratic inequalities

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Assignment 6

Solve:

4x^2+20x+25\geq0

Solution

First we solve the corresponding equation:

4x^2+20x+25=0

The left-hand side of this equation is a special product and can be written as:

(2x+5)^2=0

The solution of this equation is:

x=-\displaystyle\frac{5}{2}

The graph of the function in the left-hand side of the inequality is an 'opens up' parabola and has only one point in common with the X-axis.
The solution of the equation x=-\displaystyle\frac{5}{2} satisfies the inequality.

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