Question

what whould be the graphycal representation of (4-x)(x-2)<0

Answer 1

it is based on the concept of inequality.

given, (4 - x)(x - 2)< 0

after solving you will get, x > 4 or x < 2

now, resolving of expression for drawing graph,

(4 - x)(x - 2) < 0

or, 4x - 8 - x² + 2x < 0

or, -x² + 6x - 8 < 0

or, x² - 6x + 8 > 0 , here it is clear the expression is quadratic.

so, graph of (4 - x)(x - 2) < 0 is parabolic but condition is that graph presents for x >4 or x<2 as shown in shaded region of figure.