Question

Find all the real zeros of the function.

Answer 1

For the expression as a whole to equal zero, any of the three terms could equal zero ie:


`-2x=0` or
`x-2=0` or
`x^(2)-25=0`

We can find one zero by solving each in turn:


`-2x=0`

`x=0`


`x-2=0`

`x=2`


`x^(2)-25=0`

`x^(2)=25`

`x=√(25)=5`

The zeros are 0,2 and 5.

To check, plug back into the original equation and verify that f(x)=0.