Question

How do you factor the trinomial `2 x^2+ 5 x +12`?

Answer 1

It is `2(x+5/4+1/4*i*sqrt(71))(x+5/4-1/4*i*sqrt(71))`

Explanation:

Solving the equation `2x^2+5x+12=0` we get
dividingh by `2`:
`x^2+5/2x+6=0`
Using the quadratic formula:
`x_{1,2}=-5/4\pm\sqrt(25/16-6)`
The radicand gives:
`25/16-96/16=-71/16`
so we get
`x_{1,2}-5/4+1/4isqrt(71)`
where `i^2=-1`