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