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.

What have you tried so far? What relationships do you have between the sums and products of the roots and the coefficients? — ConMan, Sep 16 '16 at 03:03
r+s=b/a rs=c/a r+s=a
However, if you make a=b/a, you get an imaginary number for the answer of a, so I am confused. — 1pokepie, Sep 16 '16 at 03:05

score 1 · Answer 1 · answered Sep 16 '16 at 03:11

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

answered Sep 16 '16 at 03:11

Siong Thye Goh

149,520
20
88
149

However, r+s=-b/a, then -b/a = a. Thus, -b=a^2 and a = imaginary – 1pokepie Sep 16 '16 at 03:14
But I feel like your answer is the best - love you – 1pokepie Sep 16 '16 at 03:14
hmm... $b$ can be negative right? Hence $-b$ could be positive. – Siong Thye Goh Sep 16 '16 at 05:16

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

1 Answers1