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algebra senior

Problem

The two roots of the equation

a (b - c) x^{2} + b (c - a) x + c (a - b) = 0

are

1

and:

(A)

\frac{b ( c - a )}{a ( b - c )}

(B)

\frac{a ( b - c )}{c ( a - b )}

(C)

\frac{a ( b - c )}{b ( c - a )}

(D)

\frac{c ( a - b )}{a ( b - c )}

Solution

Let the other root be

k

. Then by Vieta's Formulas,

k \cdot 1 = \frac{c ( a - b )}{a ( b - c )}

,

\frac{c ( a - b )}{a ( b - c )}

Final answer

D