Question

X⁴-6x³-26x²+138x-35 when its two zerores are 2+√3

Answer 1

Since 2+√3 is a zero, x-(2+√3) is a factor of the polynomial. 
Since 2-√3 is a zero, x-(2-√3) is a factor of the polynomial. 

This means that (x-2-√3)(x-2+√3) is a factor. 

(x-2-√3)(x-2+√3) = (x-2)² - (√3)² = x² -4x +4 - 3 = x²-4x+1 

So x²-4x+1 is a factor of your polynomial. 

Divide your polynomial by x²-4x+1, using synthetic division. 

x⁴ -6x³-26x²+138x-35 = (x²-4x+1)(x²-2x-35) 

So to find other zeros, you need to solve 

x²-2x-35 = 0 
(x-7)(x+5)=0 
x=7 or x=-5

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