If α and β are the roots of the equations ax 2+ bx + c =0, α β=3 and a , b , c are in A.P., then (α2+β2) is equal to

Question

If α and β are the roots of the equations ax 2+ bx + c =0, α β=3 and a , b , c are in A.P., then (α2+β2) is equal to (A) 2 (B) -2 (C) α3+β3 (D) α+β

Tardigrade Admin · Accepted Answer

Let α+β=-(b/a) ; α β=(c/a)=3 ⇒ c=3 a...(i) text and 2 b = a + c ....(ii) ⇒ b =2 a text from(i) and (ii) ∴ α+β=-2 α2+β2=(α+β)2-2 α β =4-2 ⋅ 3=4-6=-2

Q. If $α$ and $β$ are the roots of the equations $a x^{2} + b x + c = 0, α β = 3$ and $a, b, c$ are in A.P., then $(α^{2} + β^{2})$ is equal to