Question

find a cubic function with the given zeros

square root of 6, negative square root of 6, -3

Answer 1

if x= a is a zero, then
\((x-a)\) is the factor of f(x).

similarly, if \(x= \sqrt 6\) is a zero,
\((x-\sqrt 6)\) would be the factor of f(x)

did u get this?
now can you tell me other 2 factors of f(x) ?

Answer 2

Here is another factor (it is given in the problem) Using the info furnished by hartnn. \[x+\sqrt{6}\]

Answer 3

Can you see what the third one (factor) would be?

Answer 4

It is (x+3) That is the three factors which produce those three given zeroes. Now the problem is asking for the function, all you have to do is to multiply those three factors and voila you will have the cubic function.
\[f(x)=(x-\sqrt{6})(x+\sqrt{6})(x+3)\]

Answer 5

The first two factors when multiplied be comes the familiar "difference of squares) or \[(x ^{2}-6)\]Now multiply that by x+3 and you will have the answer.

Answer 6

What did you get?