How do you determine whether #4x^2-3x+9# is a perfect square trinomial?

1 Answer
Jul 2, 2017

Answer:

#4x^2-3x+9# is not a perfect trinomial.

Explanation:

Let us discuss the identity #(a+-b)^2=a^2+-2ab+b^2#

Observe the RHS. While

  • #a^2# is the square of the first term #a#
  • #b^2# is the square of the second term #b#
  • sign of #a^2# and #b^2# is same and is positive
  • #2ab# is twice the product of two terms #a# and #b# and its sign is #+# or #-# depending on its sign in #(a+-b)^2#

In #4x^2-3x+9#, while #4x^2=(2x)^2# and #9=3^2#,

but (leaving the sign) middle term is not #2xx2x xx3# which is #12x# but is #3x#

Hence, #4x^2-3x+9# is not a perfect trinomial.