If two zeroes of the polynomial x^4+x^3-15x^2-29x-6 and 2+_√5 find other zeroes

If two zeroes of the polynomial x^4+x^3-15x^2-29x-6 and 2+_√5 find o

1.	If two zeroes of the polynomial x^4+x^3-15x^2-29x-6 and 2+_√5 find other zeroes
Answer» Two zeroes of given equation arex=2+√5 & x=2-√5=0x-2-√5=0 & x-2+√5=0Both are the factors of the given poly.=[(x-2)-(√5)]×[(x-2)+(√5)]= (x-2)^2 - (√5)^2 [ Since (a+b)(a-b)=a^2-b^2]= x^2 - 4x + 4 - 5= x^2 - 4x - 1 = 0 ...(1) Dividing the given poly. By eq. (1), we get, x^4 + x^3 - 15x^2 - 29x -6 ---------------------------------- x^2 -4x - 1=x^2 +5x + 6=0Above equation is another factor of given equationBy solving it,=x^2 + 3x + 2x + 6 = 0=x(x + 3) + 2(x +3) = 0=(x+3) (x+2) = 0x+3=0 & x+2=0x=-3 & x= -2 x = -3,-2 are another\'s zeroes of the given poly. Given equation.x^4 + x^3 - 15x^2 - 29x - 6