170621

Question : Find all the zeroes of the polynomial 2x⁴-3x³-3x²+6x-2, if two of its zeros are 5+√3 and 5-√3.

Doubt by Yathartha

Solution : 

p(x) = 2x⁴-3x³-3x²+6x-2

x=5+√3 and x=5-√3
x = 5 ± √3
x-5 = ±√3
Squaring both sides
(x-5)²=3
x²+25-10x=3
x²-10x+25-3=0
x²-10x+22=0
g(x) = x²-10x+22

Dividing p(x) by g(x)

2x⁴-3x³-3x²+6x-2 / x²-10x+22

Do it yourself.