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

1 Answer
Alan P.
Feb 19, 2016

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

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