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

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) (Show Source): You can put this solution on YOUR website!

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.

discriminant, ----------Negative value.
NO real roots.

-
(fixed)
Answer by ikleyn(52781) (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)*(2-x) = 4, 6x -3x^2 - 4 +2x = 4, -3x^2 +8x - 8 = 0, ====> 3x^2 -8x + 8 = 0, discriminant d = = 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.

RELATED QUESTIONS
2. Calculate the discriminant to determine the number of real roots. y = x^2 + 3x + 9 (answered by MathLover1)
Which describes the number and type of roots of the equation x^2 - 625 = 0? a. 1 real (answered by checkley77)
Find the exact number of real roots of the equation x^6-x^3+2x^2-3x-1=0... (answered by lwsshak3)
Calculate the discriminant to determine the number of real roots. y = x2 + 3x + 9... (answered by stanbon)
Which describes the number and type of roots of the equation x^2 + 121x = 0 a) 1 real... (answered by richwmiller)
How do we determine the number of real roots of an equation? can you determine the... (answered by jim_thompson5910)
Which describes the number and type of roots of the equation x^2 + 121x = 0 a) 1 real... (answered by richwmiller)
The number of real roots of the equation x^2-4x+4=0 is 1 2 3... (answered by Alan3354,ikleyn)
Given 3x^2+(k+2)x=-3, determine the value(s) of k so that the equation has real and equal (answered by stanbon)