Solve : x^2 - 4x + 3 < 0

I need to graph the solution also

Printable View

- Apr 7th 2005, 04:01 PMBrian D[SOLVED] Sign of a Quadratic
Solve : x^2 - 4x + 3 < 0

I need to graph the solution also - Apr 8th 2005, 02:34 AMpaultwangQuote:

Originally Posted by**Brian D**

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

(2) Think, when is (x-3)*(x-1) negative (less than zero)? When each parenthetical group has a different sign.

Possibilities:

(a) x<3 making (x-3) negative AND x>1 making (x-1) positive

(b) x>3 making (x-3) positive AND x<1 making (x-1) negative

Therefore, 1<x<3

On a number line, open circles at 1 and 3 and connect them. - Apr 21st 2005, 06:47 AMHallsofIvy
The simplest way to solve "complicated" inequalities is to solve the EQUATION. Where something is EQUAL to 0 separates where it is positive from where it is negative! (If your inequality involves fractions, you want to check points where the denominator is 0 also.)

x^2- 4x+ 3= (x- 3)(x- 1)= 0 when x= 3 or x= 1.

Now check a value in each of the three intervals x< 1, 1< x< 3, 3< x.

0 is less than 1 and 0^2- 4(0)+ 3= 3 which is positive.

2 is between 1 and 3 and 2^2- 4(2)+ 3= 4- 8+ 3= -1 which is negative

4 is larger than 3 and 4^2- 4(4)+ 3= 16- 16+ 3= 3 which is positive.

We now know that x^2- 4x+ 3 is negative for ALL numbers between 1 and 3 and negative for ALL numbers less than 1 or larger than 3. - Apr 21st 2005, 10:45 AMticbolTo HallsofIvy
You are wrong!

"...and negative for ALL numbers less than 1 or larger than 3."

Yeah? - Apr 21st 2005, 10:51 AMMathManQuote:

Originally Posted by**ticbol**

We all make mistakes - Apr 21st 2005, 12:17 PMticbolTo MathMan
I did not start it.

HallsofIvy blew in here like he could tell me something.