How do you factor this and use the zero product property to find the roots?

Factor and use the zero product to find the roots of the following quadratic equations.
a.) #0=x^2-7x+12#
b.) #0=6x^2-23x+20#
c.) #0=x^2-9#
d.) #0=x^2+12x+36#

1 Answer
Feb 28, 2018

Only answering for question a

#x= 3 and 4#

Explanation:

Given: #x^2-7x+12#

Lets look at the factors of 12

Need factors of 12 that we can sum to give #-7#

#(+-1)xx(+-12) larr" No good for 7"#
#(+-2)xx(+-6) larr" No good for 7"#

This one works
#(+-3)xx(+-4) #

#-3-4=-7 and (-3)xx(-4)=+12#

So we have: #(x-3)(x-4)=0#

Condition 1: #0xx(x-4)=0 => (x-3)=0" thus " x=+3#
Condition 2: #(x-3)xx0=0 =>(x-4)=0" thus "x=+4#

Tony B