Solve the inequality 4x^2​>5x-1

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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

Christopher L. A Level Further Mathematics tutor, A Level Maths tutor...

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