Question

How do I solve for the role of 0 in this equation?(x²-9)(x³-8)=0

Answer 1

Given the equation

`(x^2-9)\cdot(x^3-8)=0`

you should have in mind that the expression x^2-9 and x^3-8 are "numbers" and that the product of two numbers is zero if and only if one of the numbers is zero. Then, by using this, you get the following auxiliary equations

`x^2-9=0`

which is equivalent to

`x=\sqrt[]{9}`

so x=3 o x=-3.

Finally, for the other case

`x^3-8=0`

So

`x=\sqrt[3]{8}=2`

so the three possible solutions for the equation are x=3, x=-3 and x=2