Question

Find the ranges of values for which x²-5+6<0

Answer 1

The range of values of x for which the function is < 0 is:

2<x<3.

Explanation:

x²-5x+6<0

First find the critical points:

x^2 - 5x + 6 = 0

(x - 2)(x - 3) = 0.

x = 2, 3.

The critical points are 2 and 3.

Make a table of values:

x x<2 2<x<3 x >3

x -2 < 0 >0 >0

x -3 <0 <0 >0

(x - 2)(x - 3) >0 <0 >0