Question

Find a cubic function with the given zeros.
√2, -√2, -2

Answer 1

First write the function in terms of it factors, since you know it's zeros, so you have
\[(x-\sqrt{2})(x-a)(x-b)=?\]
Where a and b are the second and third root, then just expand this and you will have your function.

Answer 2

Can you help me expand it ?

Answer 3

You can try it first and I'll check if you did it right

Answer 4

So to be clear \(a=-\sqrt{2}\) (the second root) and \(b=-2\) (the third root).

Answer 5

x^3 - bx^2 -ax^2 +abx - sqrt(2)x^2 + sqrt(2)bx + sqrt(2)ax - sqrt(2)ab ? @dape

Answer 6

Let's see.

Answer 7

You should put in the zeros for \(a\) and \(b\), the first thing I wrote was just an example.

Answer 8

In general you would have (x-a)(x-b)(x-c), but here you know the three zeros a, b and c, so you should use those numbers instead of the symbols.

Answer 9

So a function with the given zeros are \(f(x)=(x-\sqrt{2})(x+\sqrt{2})(x+2)\), since if you put in \(x=\pm\sqrt{2}\) or \(x=-2\) you get zero. So you should expand this thing to get the (same) function with \(x^3\)'s in it.