Question

How do you find the roots for `20x^2 + 13x + 2`?

Answer 1

Either factor or use the quadratic formula to obtain
`x in {-1/4,-2/5}`

Explanation:

Using the quadratic formula (this can sometimes be faster if the factors are not obvious)
`color(white)("XXX")x=(-b+-sqrt(b^2-4ac))/(2a)`
in this case
`color(white)("XXX")x=(-13+-sqrt(169-160))/40=(-13+-3)/40`

`color(white)("XXX")x= -10/40= -1/4` or `x=-16/40=-2/5`

Factoring
`20x^2+13x+2 = (4x+1)(5x+2)`
The roots are the values of `x` for which the expression `=0`
So
`color(white)("XXX")(4x+1)=0 rarr x=-1/4`
or
`color(white)("XXX")(5x+2)=0 rarr x=-2/5`