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
CL
Related Maths A Level answers
All answers ▸A curve has equation y = (x-1)e^(-3x). The curve has a stationary point M. Show that the x-coordinate of M is 4/3.
Find the value of: d/dx(x^2*sin(x))
Tom drink drives two days a week, the chance of him being caught per day is 1 in 100. What is the chance he will not be driving after a) one week? b) one year?
Solve the simultaneous equations x + y = 1 , x^2 -2xy+y^2=9