Question

Quadtratic ineqalities jee positive negative positive

Answer 1

How do you solve this JEE level quadratic equation?

At times when you aren't sure of how to factorise the function and/or don't have time to do that, smart hit and trial can save your life :

Considering this function,

For -ve numbers it is trivially positive since all 5 terms are +ve for the negative numbers.

For 0 , again it is trivially positive.

For + ve numbers we can have 2 options, x < 1 in which the lower powers will have higher magnitude and x > 1 when higher powers will have higher magnitude. (For 1, it is again trivially +ve)

For case 1 : 1 > x and x^2 > x^5, so even without taking x^8 into account the function is + ve.

For case 2 : x^8 > x^5 and x^2 > x, so even without taking 1 into account the function is +ve.