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

1 Answer
Feb 19, 2016

Answer:

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#