If two zeroes of polynomial f(x)=x^4-6x^3-26x^2+138x-35 are 2+√3&2-√3. Find other zeroes

If two zeroes of polynomial f(x)=x^4-6x^3-26x^2+138x-35 are 2+√3&2-�

1.	If two zeroes of polynomial f(x)=x^4-6x^3-26x^2+138x-35 are 2+√3&2-√3. Find other zeroes
Answer» Two zeros are {tex}2\\pm\\sqrt3{/tex}Sum of Zeroes\xa0{tex}2 + \\sqrt { 3 } + 2 - \\sqrt { 3 } = 4{/tex}and product of zeroes =\xa0{tex}( 2 + \\sqrt { 3 } ) ( 2 - \\sqrt { 3 } ) = 4 - 3 = 1{/tex}Hence quadratic polynomial formed out of this will be a factor of given polynomial,So, x2 - (sum of zeroes)x + product of zeroes= x2 - 4x + 1 will be a factor of given polynomial,Divide given polynomial with x2 - 4x + 1 to get other zeroes.Now,x2 -2x - 35= x2 - 7x + 5x - 35= x(x - 7) + 5(x - 7)= (x - 5) (x - 7){tex}\\therefore {/tex}\xa0Zeros arex = 7 and x = -5{tex}\\therefore {/tex} Other two zeros are 7 and -5\xa0