Question

Find other zeroes of 2x^4-9x^3+5x^2+3x-1 if two of it zeroes are 2+root3 and 2-root3

Answer 1

Hi,

$(x-(2+\sqrt{3} )) (x-(2-\sqrt{3} ))=x^2-4x+1\\ 2x^4-9x^3+5x^2+3x-1=(x^2-4x+1)(2x²-x-1)\\ =(x^2-4x+1)(x-1)(2x+1)\\ =(x-(2+\sqrt{3} )) (x-(2-\sqrt{3} ))(x-1)(2x+1)$

Other roots are x=1 and x=-1/2.