Question

Emma wants to write a function of the least degree and rational coefficient of 1 and the zeros 3,-1, and the square root of 3. Emma said the function was cubic. a) do you agree or disagree. Why or why not? b) Write a polynomial that meets Emma's requirements.

Answer 1

A) I agree with Emma

B) x³ - (2 + √2)x² + (1 + 2√2)x - √2

Explanation:

A) We are told that the zeros are; 3, -1 and √ 3.

This means that the factors are;

(x - 3), (x + 1), (x - √2)

Now,we can see that we have 3 number of the x coefficient. It means the polynomial will have a degree of 3.

Thus,it's a cubic polynomial.

So Emma is correct about it being a cubic polynomial.

B) To write the polynomial, we will multiply out the factors listed in A above.

Thus;

(x - 3) × (x + 1) × (x - √2)

(x² - 2x + 1) × (x - √2)

x³ - 2x² + x - x²√2 + 2x√2 - √2)

x³ - (2 + √2)x² + (1 + 2√2)x - √2