Question

please check my answers. thanxs!

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)

Answer 1

I 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