Question

If α and β are the zeroes of a quadratic equation x²-7x+3 , find α-β

Answer 1

p(x)=x²-7x+3

a=1;b=-7;c=3

Let α,β

α+β=-b/a=7

αβ=c/a=3

(α-β)²=α²+β²-2αβ

        =((α+β)²-2αβ)-2αβ                (As (α+β)²=α²+β²+2αβ

          =49-4(3)                                           α²+β²=(α+β)²-2αβ)

        =37

α-β=√37