Write a polynomial function of least degree with the given zero. -1+ √ 2, √ 3

f(x) = + 2x³ - 4x² - 6x + 3

Step-by-step explanation:

Note that radical zeros occur in conjugate pairs, thus

- 1 + is a zero then - 1 - is also a zero

is a zero then - is also a zero

Thus the corresponding factors are

(x - (- 1 + ) ), (x - (- 1 - ) ), (x - ), (x - (- )), that is

(x + 1 - ), (x + 1 + ), (x - ), (x + )

The polynomial is then the product of the roots

f(x) = (x + 1 - )(x + 1 + )(x - )(x + )

     = ((x + 1)² - ()²)((x² - ()²)

     = (x² + 2x + 1 - 2)(x² - 3)

     = (x² + 2x - 1)(x² - 3) ← distribute

     = - 3x² + 2x³ - 6x - x² + 3

     = + 2x³ - 4x² - 6x + 3

i think it is 70

step-by-step explanation: