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April 25, 2014

April 25, 2014

Posted by **Liz** on Wednesday, October 24, 2007 at 10:02pm.

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation.

x^2 - 6x + 5 > 0

-I got (-ininity,1) u (5, infinity)

x^2 - 3x - 18 < 0

-I got (-infinity,-3) u (6, infinity)

x^2 - 3x - 28 ¡Ü 0

-I got (-ininity,-4] u [7,infinity)

- Algebra -
**Reiny**, Wednesday, October 24, 2007 at 10:58pmI don't understand the notation in your answer, this is how I would do this question. I will do the first one.

x^2 - 6x + 5 > 0

(x-1)(x-5) > 0

giving me "separators" at x=1 and x=5

So we have 3 regions on the number line

a)all values x<1

b) all values between 1 and 5

c) all values x>5

I then take an arbitrary value in each of these regions and test if the result is positive, not really caring about the actual answer but only its sign.

a) eg. let x=0 we get (-)(-) which is positive, so x<1 works

b) let x = 4, we get (+)(-) which is negative, so that region does not work

c) x=10 we get (+)(+) which is positive so x>5 works

therefore x<1 OR x>5 is the solution

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