Question

X² + 9x + 4 = FACTORISE

Answer 1

`$-(1)/(4) (-2x-9+√(65))(2x+9+√(65))$`

Explanation:

We have a second-degree polynomial:

I will find the roots (y = 0) completing the square:

`$x^2+9x+(81)/(4)-(81)/(4)+4=0$`

`$\left(x+(9)/(2) \right)^2 -(81)/(4) +4 =0$`

`$\left(x+(9)/(2) \right)^2 -(81)/(4) +(16)/(4) =0$`

`$\left(x+(9)/(2) \right)^2 -(65)/(4) =0$`

`$\left(x+(9)/(2) \right)^2 =(65)/(4) $`

`$\left(x+(9)/(2) \right)^2 =\pm \sqrt{(65)/(4) } $`

`$x =-(9)/(2) \pm (√(65) )/(2) $`

`$x =(-9 \pm √(65) )/(2) $`

`$\boxed{x_1 =(-9 + √(65) )/(2)} $`

`$\boxed{x_2 =(-9 - √(65) )/(2)} $`