Solve the inequality 4x^2>5x-1
We first rearrange the inequality to obtain
4x2-5x+1>0
Initially we approach this as if it were 4x2-5x+1=y, looking for y=0
We then look for solutions, the most general way is to use the quadratic formula, but often we can see factors immediately.By use of the quadratic formula, x<(-b+sqrt(b2-4ac))/2a we get 1 and from x=(-b-sqrt(b2-4ac))/2a we obtain 1/4.
solutions to 4x2-5x+1=0 are therefore x=1,1/4
If we plug a value between these into the equation, say x=1/2 we have y=-1/2 and thus the inequality is solved by x<1/4 and x>1
