Question

If α and β are the Zeroes of ax²+bx+c then find α⁵+β⁵​

Answer 1

Answer:

(b^4-5ab^2c+6a^2c^2)/a^4

Step-by-step explanation:

let alpha = x and beta = y

x+y = -b/a   x*y = c/a

x^5+y^5 = (x^2)^3+(y^2)^3

=  (x^2+y^2+2xy-2xy) (x^2-xy+y^2+2xy-2xy)

=  ((x+y)^2-2xy) ((x+y)^2-3xy)

=  (b^2/a^2-2*c/a)  (b^2/a^2-3*c/a)

=  (b^2-2ac)/a^2   *   (b^2-3ac)/a^2

=  (b^4-3ab^2c-2ab^2c + 6a^2c^2)/a^4

= (b^4-5ab^2c+6a^2c^2)/a^4