Solution assignment 05 Quadratic inequalities

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Assignment 5

Solve:

$-4x^2-8x<0$

Solution

First we solve the corresponding equation:

$-4x^2-8x=0$

or:

$4x^2+8x=0$

The left-hand side can be easily factorized by factoring out $4x$ :

$4x^2+8x=4x(x+2)=0$

and thus the solutions are:

$x=0$ or $x=-2$

The graph of the function in the left-hand side of the inequality is an 'opens down' parabola and thus the following values of $x$ satisfy the inequality:

$x<-2$ or $x>0$

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Solution assignment 05 Quadratic inequalities

Assignment 5

Solution

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