Question

quadratic equation x(3x-p)=2x-3,where p is a constant, does not intersects the x -axis. find the range of values of p?

Answer 1

doesn't intersect X axis that means X is not real
I. e., roots have to b imaginary ...descriminant should be negative
3x^2-px-2x+3=0
3x^2-x(p+2)+3=0
d=√(p+2)^2-36<0
(p+2)^2<36
-6<p+2<6
-8<p<4