Factors of 9m^2+20m+104 = to

Question

factors of 9m^2+20m+104=

Answer 1

using the quadratic formula...

[-20±√(400-4*9*104)]/2*9

[-20±√(400-3744)]/18

[-20±√-3344]/18

[-20±√3344√-1]/18 where √-1=i

[-20±√(16*209)(i)]/18

[-20±4√209(i)]/18

[-10±2√209(i)]/9 are the two factors (-10+2√... and -10-2√...)

 

Answer 2

To find the factors we will need to find the roots.

 

After we have the roots... the factors will be (x-1st root)(x-2nd root)

 

We need to use the quadratic equation to find the roots.

 

{-20 +- sqrt[20²-4(9)(104)]}/2(9)

 

That yields 2 roots:

 

(-10+2 i sqrt 209) / 9 and (-10 - 2 i sqrt 209) / 9

 

The next step is to make the factors

 

the first factor:

(x- 1st root)

x -  [(-10+2 i sqrt 209) / 9]  which simplifies to (9x+10-2i sqrt209) / 9

 

The second factor:

(x - 2nd root)

x - [(-10-2i sqrt 209)/9] which simplifies to (9x+10+2i sqrt 209)/9