Find the roots of 14/(x+3) -1=5/x+1
Answers
hi mate,
14/(x+3) -1 = 5/x+1
=2x² - 3x + 15
solving -2x²+3x-15 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax²+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B²-4AC
x = ————————
2A
In our case, A = -2
B = 3
C = -15
Accordingly, B2 - 4AC =
9 - 120 =
-111
Applying the quadratic formula :
-3 ± √ -111
x = ——————
-4
In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written (a+b*i)
Both i and -i are the square roots of minus 1
Accordingly,√ -111 =
√ 111 • (-1) =
√ 111 • √ -1 =
± √ 111 • i
√ 111 , rounded to 4 decimal digits, is 10.5357
So now we are looking at:
x = ( -3 ± 10.536 i ) / -4
Two imaginary solutions :
x =(-3+√-111)/-4=(3-i√ 111 )/4= 0.7500+2.6339i
or:
x =(-3-√-111)/-4=(3+i√ 111 )/4= 0.7500-2.6339i
Two solutions were found :
x =(-3-√-111)/-4=(3+i√ 111 )/4= 0.7500-2.6339i
x =(-3+√-111)/-4=(3-i√ 111 )/4= 0.7500+2.6339i
i hope it helps you.
Answer:
here is the answer to your question
The roots are 4 and 1
