SOLUTION: 16x2 - 16x + 4 > 0 Solve each rational inequality. State and graph the solution set.

Algebra ->  Graphs -> SOLUTION: 16x2 - 16x + 4 > 0 Solve each rational inequality. State and graph the solution set.      Log On


   

Question 118879This question is from textbook Elementary and Intemediate Algebra
: 16x2 - 16x + 4 > 0 Solve each rational inequality. State and graph the solution set. This question is from textbook Elementary and Intemediate Algebra

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

16x%5E2+-+16x+%2B+4+%3E+0…..divide both sides by 4
4x%5E2+-+4x+%2B+1%3E+0…..
Solve it as an equation first:
4x%5E2+-+4x+%2B+1=+0…..
Use quadratic formula to solve for x
x%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29

x%5B1%2C2%5D=%28-%28-4%29+%2B-+sqrt+%28%28-4%29%5E2+-+4%2A4%2A1+%29%29+%2F+%282%2A4%29

x%5B1%2C2%5D=%284+%2B-+sqrt+%2816+-+16+%29%29+%2F+8

x%5B1%2C2%5D=%284+%2B-+sqrt+%280+%29%29+%2F+8

x%5B1%2C2%5D=%284+%2B-+0%29+%2F+8…………there is only one solution

x%5B1%5D=4+%2F+8

x%5B1%5D=1+%2F+2

So, your solution will be:

x+%3E+1%2F2 or (1%2F2,infinity)

Graph it, and shade everything to the right from
x=1%2F2 excluding x=1%2F2


Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-4x%2B1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-4%29%5E2-4%2A4%2A1=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-4%29%29%2F2%5C4.
Expression can be factored: 4x%5E2%2B-4x%2B1+=+%28x-0.5%29%2A%28x-0.5%29

Again, the answer is: 0.5, 0.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-4%2Ax%2B1+%29