Help on solving roots given sum of zeros, product of zeros, sum of coefficients are equal.

Question

The sum of zeros, the product of zeros, and the sum of the coefficients of the function f(x) = ax^2 +bx +c are equal. Show that all three of these quantities must equal a.

Pls help for school assignment.

Answer 1

Sum of zeros $= \frac{-b}{a}$ ( I think you made a mistake at this step)

product of zeros $=\frac{c}a$

Hence $c=-b.$

Hence $a+b+c=a+b-b=a$