Question

Find the roots of 14/(x+3) -1=5/x+1

Answer 1

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 2

Answer:

here is the answer to your question

The roots are 4 and 1