What are the roots of the equation x / (x + 2) + 3 / (x - 4).
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
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
=> 1/2 + i*sqrt 23 / 2
and 1/2 - i*sqrt 23 / 2
The required roots of the equation are:
1/2 + (i*sqrt 23) / 2 and 1/2 - (i*sqrt 23) / 2
Related Questions
- `(3/2)x - -4 = 13` Solve the equation for x.
- 1 Educator Answer
- Find the quadratic equation whose roots are at x = 3 and x = 5.
- 2 Educator Answers
- Find the equation of both lines that pass through the point (2, -3) and are tangent to the...
- 3 Educator Answers
- Determine the set of values of m for which both roots of equation x^2 - (m+1)x + m+4 = 0 are...
- 1 Educator Answer
- Find the complete factorization of P(x) = x^4-2x^3+5x^2-8x+4? the roots i found so far are :...
- 1 Educator Answer
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Let f(x) = x/(x+2) + 3/(x-4)
To find the roots, we will rewrite as one fraction.
==> f(x)= [ x(x-4) + 3(x+2) ] / (x+2)(x-4)
==> f(x) = ( x^2 - 4x + 3x + 6) / (x+2)(x-4)
==> f(x) = (x^2 -x + 6) / (x+2)(x-4)
Now the roots if f(x) are the roots of the numerator.
=> x^2 -x + 6 = 0
==> x1= ( 1 + sqrt(1 - 24) /2 = (1/2) + sqrt23 / 2
==> x2= (1/2) - sqrt23*i /2
Then the roots are:
x = { (1/2) + (sqrt23 /2) *i and (1/2) - (sqrt23 /2)*i }
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.
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Student Answers