Solution assignment 02 Quadratic inequalities

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Assignment 2

Solve:

-x^2+5x-6>0

Solution

First we solve the corresponding equation:

-x^2+5x-6=0

We can write this equation as:

x^2-5x+6=0

which can be solved quite easily by factorizing:

x^2-5x+6=(x-3)(x-2)=0

and thus the solutions are:

x_1=3 or x_2=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:

2<x<3

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