How do you list all possible roots and find all factors of #4x^2-9#?

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Answer 1 · 2016-09-28T00:50:47

Roots: #+-3/2# Factors: #(2x+3)(2x-3)#

#f(x) = 4x^2-9#

The roots of #f(x)# are the values of #x# for which #f(x)=0#

Since #f(x)# is of 2nd degree, we know that the number of roots is at most 2.

Notice that both #4x^2# and #9# are square values and remember that: #a^2-b^2 = (a+b)(a-b)#

In this example #a=2x# and #b=3#

#:. f(x) = (2x+3)(2x-3)#

#f(x) = 0# when either #(2x+3)=0# or #(2x-3)=0#

Hence the roots of #f(x)# are #+-3/2#