Question 7702
x(x - 5) > 3(1 - x)

{{{x^2 - 5x > 3 - 3x}}}
{{{x^2 - 2x -3 > 0}}}


So we have a u-shaped quadratic, which when plotted on a graph may/may not cross the x-axis: wherever it does cross, those points are the roots.


The question says (at least my version of it) "where is the quadratic equation greater than zero"... visualising the u-shape, this will be any value of x to the left of the left root and any value of x to the right of the right root.


So...we need to find the roots!


{{{x^2 - 2x - 3 = 0}}}
(x - 3)(x + 1) = 0


so EITHER x-3=0 OR x+1=0
so either x=3 or x=-1.


So where is the curve > 0?


answer is: x<-1 and x>3


jon.