please help me solve this polynomial inequality

Question

 x^ -4x+3 <0 

Answer 1

x² - 4x + 3 < 0

(x - 3)(x - 1) < 0 as stated by the other Mark M.

This is true if either

x - 3 > 0   and   x - 1 < 0

x > 3        and   x < 1

Or

x - 3 < 0   and   x - 1 > 0

x < 3        and   x > 1

 

1 < x < 3 

 

(1, 3)        (interval notation)

Answer 2

I am assuming that the inequality is x²-4x+3<0

 

To solve the inequality, we first solve the equation x²-4x+3 = 0

 

                                                                       (x-3)(x-1) = 0

 

                                                                       x = 1 or 3

 

Next, plot 1 and 3 on a number line to divide the number line into a collection of intervals.  In this problem, we get the intervals (-∞,1), (1,3), and (3,∞).

 

Choose one point from each interval, say 0, 2, and 4.  The points chosen are called test points.  Substitute each test point into x²-4x+3 (or the factored form, (x-3)(x-1)).

 

Interval      Test Point    Sign of (x-3)(x-1)

 

(-∞,1)              0              positive

 

(1,3)                2              negative

 

(3,∞)               4              positive

 

Since we are trying to solve the inequality (x-3)(x-1) < 0, we choose the intervals in the table above where the sign of (x-3)(x-1) is negative.

 

Solution:  (1,3)