Question

Factorize x^2-8x -6 and find the relationship

Answer 1

hi mate,

solution:

Solving x²-8x-6 = 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 = 1

B = -8

C = -6

Accordingly, B² - 4AC =

64 - (-24) =

88

Applying the quadratic formula :

8 ± √ 88

x = —————

2

Can √ 88 be simplified ?

Yes! The prime factorization of 88 is

2•2•2•11

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 88 = √ 2•2•2•11 =

± 2 • √ 22

√ 22 , rounded to 4 decimal digits, is 4.6904

So now we are looking at:

x = ( 8 ± 2 • 4.690 ) / 2

Two real solutions:

x =(8+√88)/2=4+√ 22 = 8.690

or:

x =(8-√88)/2=4-√ 22 = -0.690

Two solutions were found :

x =(8-√88)/2=4-√ 22 = -0.690

x =(8+√88)/2=4+√ 22 = 8.690

i hope it helps you.