Question

Find a cubic function with the given zeros. Square root of two., - Square root of two., -2 f(x) = x3 + 2x2 - 2x + 4 f(x) = x3 + 2x2 + 2x - 4 f(x) = x3 - 2x2 - 2x - 4 f(x) = x3 + 2x2 - 2x - 4\

Answer 1

Answer is:
x = 0, x = –1 with multiplicity 2

Answer 2

f(x) = x^3 + 2x^2 - 2x - 4

Explanation:

Hi!

We only need to multiply the following monomials:

(x - √2)

(x + √2)

(x + 2)

Since each of them has a zero in the required values.

Therefore:

(x - √2)*(x + √2)*(x + 2) = (x + 2)*(x^2 - 2)

*Here I have used the property:

(x-a)*(x+a) = x^2-a^2

*with a = √2

(x - √2)*(x + √2)*(x + 2) = (x + 2)*(x^2 - 2) = x^3 -2x + 2x^2 - 4

That is:

f(x) = x^3 + 2x^2 - 2x - 4

The correct answer is the third