What are all the possible rational zeros for #y=12x^2-28x+15# and how do you find all zeros?

1 Answer
Sep 2, 2016

Answer:

Zeros of #y=12x^2-28x+15# are #x=5/6# and #x=3/2#.

Explanation:

Zeros of a function #f(x)# are those values of #x#, for which #f(x)=0#.

As #y=12x^2-28x+15# can be factorized, let us do so by splitting the middle term #-28# in two parts so that their product is #12×15=180#. It is apparent that these are #-18# and #-10#.

Hence #y=12x^2-28x+15#

= #12x^2-18x-10x+15#

= #6x(3x-3)-5(2x-3)#

= #(6x-5)(2x-3)#

It is apparent that if either #6x-5=0# or #2x-3=0#, #y=12x^2-28x+15# will be zero.

Hence, zeros of #y=12x^2-28x+15# are #x=5/6# and #x=3/2#.