How do you find the missing number or term to make a perfect square trinomial. #x^2+1/3x+___ #?

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Answer 1 · 2015-06-13T23:05:25

#1/36#

you're looking for a square trinomial, which is of the form

#x^2 +2alphax+alpha^2#

Let's find #alpha^2#

#x^2 + 1/3x + alpha^2 = x^2 +2alphax+alpha^2#

Which means #1/3=2alpha => alpha=1/6#

In fact, #(x + 1/6)^2 = x^2 + 2 1/6x + 1/36 = x^2 + 1/3x+1/36#

So #alpha^2=1/36#

Answer 2 · 2015-06-13T23:08:07

Perfect square trinomials are of the form

#a^2+2ab+b^2 = (a+b)^2#.

In this case #a=x#, so #2b = 1/3#, so #b=1/6# and #b^2 = 1/36#

Compare:

#x^2+1/3x+#_

with

#a^2 + 2ab + b^2#

We can obviously put #a=x#, giving

#x^2 + 2bx + b^2#

Comparing the coefficient of #x#, we have

#2b = 1/3#

Divide both sides by #2# to get:

#b = 1/6#

So #b^2 = (1/6)^2 = 1/36#

which is the missing term.