First slide

Theory of equations

Question

The roots of the equation $a (b - c) x^{2} + b (c - a) x + c (a - b) = 0$ are

Easy

A

$\frac{c (a - b)}{a (b - c)}, \frac{b (c - a)}{c (a - b)}$
B

$\frac{b (c - a)}{c (a - b)}, 1$
C

$1, \frac{c (a - b)}{a (b - c)}$
D

$\frac{c (a - b)}{b (c - a)}, 1$

Solution

if a+b+c=0 then the roots are 1 and c/a
Sum of the Coefficients = a(b–c)+b(c–a)+c(a–b)=0
$∴$ Roots are $1, \frac{c (a - b)}{a (b - c)}$

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