SOLUTION: Determine the number of real roots of the equation 3x-2=4/(2-x)

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Question 1093399: Determine the number of real roots of the equation 3x-2=4/(2-x)
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
3x-2=4%2F%282-x%29
A value which would NOT be a root would be x=2, because the right side expression would be undefined for this value. It might or might not come up during the solution process.

%283x-2%29%282-x%29=4

6x-4%2B2x-3x%5E2-4=0

-3x%5E2%2B8x-8=0
3x%5E2-8x%2B8=0

discriminant, 8%5E2-4%2A3%2A8=64-96=-32----------Negative value.
NO real roots.









-
(fixed)

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Determine the number of real roots of the equation 3x-2=4/(2-x)
~~~~~~~~~~~~~~~~~ 

3x+-+2 = 4%2F%282-x%29  ====>

(3x-2)*(2-x) = 4,

6x -3x^2 - 4 +2x = 4,

-3x^2 +8x - 8 = 0,  ====>

3x^2 -8x + 8 = 0,

discriminant  d = 8%5E2+-+4%2A3%2A8 = 64 - 96 = -32.


Since the discriminant is NEGATIVE, there are no real solutions.


Answer.  The number of real roots of the equation 3x-2=4/(2-x) equal to 0 (zero, ZERO).


And the plot below  ILLUSTRATES  it.




Plot y = 3x-2 (red) and y = 4/(2-x) (green)


The solution by @josgarithmetic was  W R O N G.  Simply ignore it.