Question

if alpha and beta are the zeros of the polynomial fx= ax^2+bx+c
evaluate
alpha^2beta + alphabeta^2​

Answer 1

Answer:

hope it helps u

pleasure to help you

Answer 2

Answer:

(alpha^2•beta)+(alpha•beta^2) =

= (-b•c)/a^2

Step-by-step explanation :

f(x) = ax^2 + bx + c

Let the zeroes of this given polynomial be 'alpha' and 'beta'. Then, we know that,

CASE I =>

(alpha) + (beta) = -b/a

=> (alpha) + (beta) = -b/a ....(1)

CASE II =>

(alpha)•(beta) = c/a

=> (alpha)•(beta) = c/a ....(2)

Now, according to the question,

(alpha^2•beta) + (alpha•beta^2) =

= (alpha•beta)•(alpha + beta) ....(3)

From eq.(1) , eq.(2) and eq.(3) , we get,

= (c/a)•(-b/a)

= (-b•c)/a^2

Hence,

(alpha^2•beta)+(alpha•beta^2) =

= (-b•c) / a^2