How do you find the zeroes of #f(x) = (3x-5)(2x+7)#?

3 Answers
Jun 5, 2018

Answer:

#x=-7/2,x=5/3#

Explanation:

#"to find the zeros set "f(x)=0#

#(3x-5)(2x+7)=0#

#"equate each factor to zero and solve for x"#

#2x+7=0rArrx=-7/2#

#3x-5=0rArrx=5/3#

Jun 5, 2018

Answer:

Zeros are #x=5/3# and #x=-7/2#

Explanation:

Zeros, Roots and Solutions to a polynomial are all the same thing, to find the zeros we first set #f(x) =0# and then solve for x:

#f(x) = (3x-5)(2x+7)#

#0 = (3x-5)(2x+7)#

The zero product rule states that if:

#a*b=0# then #a=0# or #b=0#

#(3x-5)=0#

#3x-5=0#

#3x=5#

#x=5/3#

or

#(2x+7)=0#

#2x+7=0#

#2x=-7#

#x=-7/2#

Jun 5, 2018

Answer:

f(x)=0 when #x=5/3# and #x=-3 1/2#

Explanation:

You just have to see how f(x) can be 0. In this expression f(x) = 0 when either of the parentheses is 0, i.e. either
(3x-5)=0
or (2x+7)=0
(3x-5)=0 when 3x=5 or #x=5/3#
(2x+7)=0 when 2x=-7 or #x=-7/2=-3 1/2#