Quadratic inequalities

So I have this question:

For b, I got p = 3-2√2 and 3+2√2. The mark scheme says the answer is:

p<3-2√2 or p>3+2√2

How do I know whether to put "or" or just write it like: 3+2√2 < p < 3-2√2 ?

Reply 1

Zacken

Original post by кяя

So I have this question:

For b, I got p = 3-2√2 and 3+2√2. The mark scheme says the answer is:

p<3-2√2 or p>3+2√2

How do I know whether to put "or" or just write it like: 3+2√2 < p < 3-2√2 ?

You sketch the graph of

p^2 - 6p +1 > 0

. Always sketch the graph, it doesn't need to be elaborate, just a U if the number in front of p^2 is positive and an upside down u it's negative.

Label the roots (where it cuts the axis) as your values.

Then you know that you want the graph to be >0, that is, above the p-axis. That's precisely the region that >second root and <first root.

Had it asked you for p^2 - 6p + 12 < 0, then you would want the region where the graph is under the x-axis which is in between the two roots, so 3 - sqrt(blah) < p < blah