Quadratic with non numeric coefficents. Find where q has no real roots

Question

Be patient with me here I'm picking up prep to do my A level maths after not doing any for the last 16 years...

My question is for which values of p does the equation f(x)=0 have no real roots

px^2 - px + 3x - 4

I'm really struggling with this one, the use of non numeric cofficents here is really confusing me, can someone fill in the blanks.

Also correct terminology to my question would be helpful as I'm finding it hard to get answers to stuff like this. I'm sure this has been covered elsewhere on here but I can't find it.

Thanks so much

Answer 1

Guide:

For a quadratic equation to have no real roots, the discriminant is negative.

Let me rewrite $px^2-px+3x-4 = px^2+(3-p)x-4$

Try to write down the discriminant and find the corresponding region.