Question

If 1+√3 & 1-√3 are zeroes of x^3-3x^2+2, find the third zero

Answer 1

Step-by-step explanation:

first ,find sum and product of given zeroes

α+β=1+√3+1-√3. And αβ=1²-√3²

Second,form a polynomial with the sum and product of given zeroes

X²-2x-2 [ x^2-(α+β)x+(αβ)]

Third, Divide x³-3x²+2 by x²-2x-2

Fourth,on dividing we get a quotient ,then factorise the obtained quotient

Here quotient is x-1 ,by factorising it we get x=1

Hence, third zero is 1