Question

The roots of the equation $a{x}^2+bx+c=0$ will be in reciprocal if:

• A. $a=b$
• B. $a=bc$
• C. $c=a$
• D. $c=b$

Answer 1

The correct option is C $c=a$

Given quadratic equations is $a{x}^2+bx+c=0$

Sum of the roots of the equation is $-\frac{b}{a}$

Product of the roots is $\frac{c}{a}$

The roots will be in reciprocal if product of the roots $=1$

$\Rightarrow \frac{c}{a}=1$

$\therefore c=a$