Question

Algebraically determine the exact roots:
4x-1/x = 2x/3
help please? :(
Midterm tomorrow!

Answer 1

\[\frac{ 4x-1 }{ x }=\frac{ 2x }{ 3 }\]
Cross multiply.
\[3(4x-1)=2x(x)\]
\[12x-3=2x^2\]
Move everything to the RHS (Right Hand Side)
\[2x^2-12x+3=0\]
Solve the quadratic.

Answer 2

Using the quadratic formula*

Answer 3

thank you! :)

Answer 4

The root of the equation is when the graph of the function crosses the x axis. It is also where y = 0. So, just solve for x.

4x -1/x = 2x/3

4x^2 -1 = (2/3)(x^2)

4x^2 - (2/3)(x^2) - 1 = 0

12x^2 - 2x^2 -3 = 0

10 x^2 = 3

x^2 = 3/10

x = plus or minus sqrt(3/10)