First slide

Theory of equations

Question

Both the roots of the equation $(x - a) (x - b) + (x - b) (x - c) + (x - c) (x - a) = 0$ are always

Moderate

A

positive
B

negative
C

real
D

none of these

Solution

The given equation can be written as
$3 x^{2} - 2 x (a + b + c) + a b + b c + c a = 0$
Let D be its discriminant. Then
$\begin{array}{l} D = 4 (a + b + c)^{2} - 12 (a b + b c + c a) \\ \Rightarrow D = 2 \{(b - c)^{2} + (c - a)^{2} + (a - b)^{2}\} > 0 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App