SOLUTION: I really need an understanding on Quadratics and discriminants: Could some one help me understand this problem? The instructions are to solve the inequality. State the solution

Question 18721: I really need an understanding on Quadratics and discriminants: Could some one help me understand this problem?
The instructions are to solve the inequality. State the solution set using interval notation and graph it:
x - x^2 is less than or equal to 0
Thanks!

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
SEE THIS EXAMPLE WHICH IS MORE COMPLEX AND EXPLANATION TO SOLVE YOUR PROBLEM
x - 2/x + 3 is less than 1
let y=(x - 2/x + 3)<1
x - 2/x + 3-1<0 ....or....x - 2/x + 2<0
(x^2-2+2x)/x<0...or ...(x^2+2x-2)/x<0..
now a fraction will be -ve (<0)if n.r and d.r are of different signs..let us take the 2 cases
dr=x is +ve...then nr should be -ve
dr=x is -ve...then nr should be +ve.
now solve the nr using quadratic formula

hence x=(-1+sqrt3)/2...and....(-1-sqrt3)/2..for conveinience if we call these 2 values as p(approximately=-1.37)and q(approximately=0.37),we find that if x lies between p and q (-1.37 and 0.37 )nr is -ve and when x is less than
p(-1.37) or greater than q(0.37) ,nr is +ve.
now we have to combine this with the above assumption on dr
dr=x is +ve...then nr should be -ve..so x should be between 0 and (-1+sqrt3)/2(not -1.37 to zero as x is already taken as positive)
dr=x is -ve...then nr should be +ve.so x should be less than ....(-1-sqrt3)/2..
(not 0.37 to zero as x is already taken as negative)

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