Question

The roots of the equation $(a+c-b)x^2+2cx+(b+c-a)=0$, where $(a,b,c)\in R$ and $(a\ne b)$ are

• A. real and distinct
• B. real and equal
• C. real
• D. imaginary

Answer 1

The correct option is A real and distinct

$f\left(x\right)=(a+c-b)x^2+2cx+(b+c-a)$
$f(-1)=a+c-b-2c+b+c-a$
$=2c-2c=0$
$\therefore$ $-1$ is a root of the given equation .
The product of roots is $\frac{(b+c-a)}{(a+c-b)}$
$-1\times x_2=\frac{(b+c-a)}{(a+c-b)}$
$x_2=\frac{(a-c-b)}{a+c-b}$
$\therefore$ Two roots are real and distinct .