Question

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

Answer 1

`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`

Answer 2

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`

Answer 3

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`