EDEXCEL - C1 paper HELP

Hello,
Could someone help me on how to go about answering the question please.

8) The straight line with equation y = 3x – 7 does not cross or touch the curve with equation y = 2px^2 – 6px + 4p, where p is a constant.

(a) Show that 4p^2 – 20p + 9 < 0

(b) Hence find the set of possible values of p.

Thank you!

To find the points of intersection you would solve the equations simultaneously (set the equations equal to each other) to give

$3x-7=2px^2-6px+4p$

If you are told that the lines don't intersect then the equation above can't have any solutions. So if the equation has no solutions, what can you say?

Yes, I thought if the equations do not touch/meet, then I would not be able to equate them. However, for part A , the mark scheme has equated the equations?!?

I can link the mark scheme, if that helps...

http://qualifications.pearson.com/content/dam/pdf/A-Level/Mathematics/2013/Exam-materials/6663_01_rms_20160817.pdf

No I am saying that you should be equating the equations. Then once you've done that you need to show that the equation that you've made has no solutions.

Hint : discriminant.