Question

If the roots of the equation $(b-c)x^2+(c-a)x+(a-b)=0$ are real and equal, then:

• A. $2b=a+c$
• B. $2a=b+c$
• C. $2c=a+b$
• D. None of these

Answer 1

The correct option is A $2b=a+c$

Given equation is $(b-c)x^2+(c-a)x+(a-b)=0$

Sum of the coefficients$=b-c+c-a+a-b=0$

Thus, one root is $=1$

Product of the roots$=\frac{a-b}{b-c}$

Given that the roots are equal.

Root are $1\times 1=\frac{a-b}{b-c}$

$\Rightarrow b-c=a-b$

$\Rightarrow 2b=a+c$

Hence $2b=a+c$