Form the values of the following in terms of a, b, c if `alpha, beta` are roots of `ax^(2)+bx+c=0`, `c != 0`
i) `(1)/(alpha)+(1)/(beta)`
ii) `(1)/(alpha^(2))+(1)/(beta^(2))`
iii) `alpha^(3)+beta^(3)`
iv) `((alpha)/(beta)-(beta)/(alpha))^(2)`
v) `alpha^(4)beta^(7)+alpha^(7)beta^(4)` vi) `alpha^(2)+beta^(2)`
vii) `(alpha^(2)+beta^(2))/(alpha^(-2)+beta^(-2))`
viii) `(alpha)/(beta^(2))+(beta)/(alpha^(2))`

Answer

i) `(-b)/(a)` ii) `(b^(2)-2ac)/(c^(2))` iii) `(3abc-b^(3))/(a^(3))` iv) `(b^(2)(b^(2)-4ac))/(a^(2)c^(2))` v) `bc^(4)((3ac-b^(2)))/(a^(7))` vi) `(b^(2)-2ac)/(a^(2))` vii) `(c^(2))/(a^(2))` viii) `(3abc-b^(3))/(ac^(2))`