Question

find all the zeros of 2x^4 - 9x^3 + 5x^2 + 3x - 1 if two of its zeros are 2+√3 and 2-√3

Answer 1

(2+√3) and (2-√3) are the 0's of the polynomial
⇒ [x - (2+√3)] and [x - (2-√3)] are the factors
[x - (2+√3)] [x - (2-√3)] = x2 - 4x + 1
(2x⁴ - 9x³ + 5x² + 3x - 1) ÷ (x² - 4x + 1)
= (2x₂ - x - 1)
=(2x² - x - 1) 
=2x²-2x+x-1
=2x(x-1)+1(x-1)
=(2x+1)(x-1)
∴ The the other two 0's are -1/2 and 1 .

Answer 2

Answer is attached below