Question

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

• A. $a+b+c$ & $a-b+c$
• B. $\frac{1}{2}$ & $a-2b+c$
• C. $a-2b+c$ & $\frac{1}{(a+b-2c)}$
• D. none of these

Answer 1

Answer: (D)

none of these

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

Now, here the sum of coefficients $=0$
$\therefore$ One root is $1$.

Let $\alpha$ be the other root.

$\Rightarrow 1.\alpha =\frac{a-2b+c}{a+b-2c}$

$\Rightarrow \alpha =\frac{a-2b+c}{a+b-2c}$

So, the roots are $1,\frac{a-2b+c}{a+b-2c}$.