Question

Find the zeroes of the polynomial in g(x)= 3-6x ?

Answer 1

`x = 1/2`

Explanation:

A theorem states that every polynomial of degree `n` as exactly `n` solutions in the complex field.

If you don't know what complex numbers are, you just have to know that, if you use real numbers, you will find no more than `n` solutions for a polynomial of degree `n`.

In this case, we have a polynomial of degree `1`, so it can only have one solution.

To find it, we need to find a value for `x`, say `x_0`, such that

`g(x_0) = 0`

Since `g(x) = 3-6x`, we want to solve `3-6x=0`

If you add `6x` to both sides, you will get

`3 = 6x`

and dividing both sides by `6` you get

`\frac{3}{6} = x`

since `\frac{3}{6} = \frac{1}{2}`, the solution (or zero, or root) of this polynomial is

`x = 1/2`

Answer 2

`x=1/2`

Explanation:

Given: `3-6x=0`.

Adding `6x` to both sides yields:

`3-color(red)cancelcolor(black)(6x)+color(red)cancelcolor(black)(6x)=6x`

`3=6x`

Divide by `6` gets us `x`, which equals to:

`3/6=x`

`x=1/2`