How do you solve 4x^2 - 4x + 1 > 4 ? |
First, consider solving the quadratic equation:
4x^{2} - 4x + 1 = 4
The first step is to collect all the terms together, leaving '=0' on the right hand side:
4x^{2} - 4x - 3 = 0
Solving by factorisation:
(2x - 3) (2x + 1) = 0
2x - 3 = 0 or 2x + 1 = 0
x = 1.5 or x = -0.5
But we wish to solve the inequality:
4x^{2} - 4x - 3 > 0
Now consider a sketch of the graph y = 4x^{2} - 4x - 3 (right).
The graph (a 'U'-shaped parabola) shows that the function is greater than zero
to the left of the root at -0.5 and
to the right of the root at 1.5
So the solution to the equation x^{2} - 4x + 1 > 4 is:
x < -0.5 or x > 1.5 |