What are the roots of the equation x / (x + 2) + 3 / (x - 4).

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justaguide eNotes educator | Certified Educator

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What you have given is an expression. Equating it to 0, the roots have been calculated.

x / (x + 2) + 3 / (x - 4) = 0

=> x( x - 4) + 3(x + 2) = 0

=> x^2 - 4x + 6 + 3x = 0

=> x^2 - x + 6 = 0

The roots of this equation are

[ 1 + sqrt (1^2 - 24) ] /2

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hala718 eNotes educator | Certified Educator

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neela | Student

Question: What are the roots of the equation x / (x + 2) + 3 / (x -4) = 0.(edited please).

A:

We multiply both sides by (x+2)(x-4):

x(x-4) + 3(x+2) = 0.

x^2-4x+3x +6 = 0.

x^2-x+6 = 0.

We know that ax^2+bx+c = 0 has roots:

x1 = {-b+(b^2-4ac)^(1/2)}/2a or x2 = {-b-(b^2-4ac)^(1/2)}/2a.

So x^2-x+3 has roots:

x1  = {-(-1)+(1-4*1*6)^(1/2)}/2  = {1+(-23)^(1/2)}/2, or

x2 = {1-(-23)^(1/2)}/2.

So the roots are x1 = {1+(-23)^(1/2)}/2 and x2 = {1-(-23)^(1/2)}/2.

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