Question

Obtain all zeros of the polynomial f(x) = x⁴ – 3x³ – x² + 9x – 6 if two of its zeros are –√3 and √3 .

Answer 1

x = 1 and x = 2.

Step-by-step explanation:

Polynomial f(x) = x⁴ – 3x³ – x² + 9x - 6

–√3 and √3 are zeroes of the polynomial.

Then (x+√3) and (x+√3) are factors of the polynomial and they divide the polynomial.

So (x+√3)*(x+√3) = x²-3

x⁴ – 3x³ – x² + 9x - 6 / (x²-3) = x² −3x +2  

Now let's factorize x² −3x +2  

x² −3x +2 = 0

x² -x -2x +2 = 0

x (x-1) -2 (x-1) = 0

(x-1) (x-2) = 0

So the other roots are x = 1 and x = 2.

Answer 2

Answer:

Step-by-step explanation:

Sry dont know