Question

Middle term splitting of x²-x-1

Answer 1

Hope this answer helps!

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 = 1

B = -1

C = -1

Accordingly, B² - 4AC =

1 - (-4) =

5

Applying the quadratic formula :

1 ± √ 5

x = ————

2

√ 5 , rounded to 4 decimal digits, is 2.2361

So now we are looking at:

x = ( 1 ± 2.236 ) / 2

Two real solutions:

x =(1+√5)/2= 1.618

or:

x =(1-√5)/2=-0.618