Question

α,β are roots of y²-2y-7=0 find,α³-β³=?

Answer 1

Answer:

Hope this helps you : )

since α and β are roots of the given equation ,

we know that for a quadratic equation ax^2 + bx + c:

sum of roots = -b/c

product of roots = c/a

∴ α+β = -(-2) = 2 ; -------> (i)

αβ = -7 ;--------> (ii)

∴ we can write ,  α³- β³ = (α+β)³ - 3α²β - 3αβ²

                                      = (α+β)³ - 3αβ(α+β) [ from equation (i) & (ii) ]

                                      = 2³ - 3*(-7)*2

                                      = 8 + 42

                                      = 50 (Ans)