solve the polynomial inequality

Question

x² -4x+3>0

 

 

 

use polynomial inequalities to solve 

Answer 1

First, factor out the polynomial:

 

x^2 -4x + 3 = (x-1)(x-3)

 

(x-1)(x-3) > 0

 

Then both factors must be positive or both must be negative:

 

Case 1.  Both positive: x>1 and x>3.  x>3 satisfies both conditions.

 

Case 2.  Both negative: x<1 and x<3.  x<1 satisfies both conditions.

 

Combining the above,

 

x<1 and x>3 satisfy the inequality.