Question

If the roots of the equation $a{x}^2+bx+c=0$ are reciprocal to each other, then

• A. $a+c=0$
• B. $b=0$
• C. $a-c=0$
• D. None of these

Answer 1

Answer: (C)

$a-c=0$

Roots of the equation $a{x}^2+bx+c=0$ are reciprocal to each other,

i.e $\alpha ,\frac{1}{\alpha }$ are the roots.

Product of roots $\alpha \frac{1}{\alpha }=\frac{c}{a}$

$\Rightarrow a=c$

Hence, option C.