Question

find the zeroes of the following quadratic polynomials X²-4√3x+3

Answer 1

P(x) = x²-4√3x+3 
α,β are zeroes of polynomial P(x).
In a quadratic polynomial ax²+bx+c=0
Sum of zeroes α,β is
α+β=-b/a 
Product of zeroes
αβ=c/a.
Now comparing ax²+bx+c with x²-4√3x+3 
we get a=1 b=-4√3 c=3
α+β-αβ=-b/a-c/a = -(-4√3)-3/1= 4√3-3.
So, α+β-αβ=4√3-3.