Question

For the equation $x^2+bx+c=0,$ if $1+b+c=0$ for all $b,c\in R,$ then the roots are

• A. $1$
• B. $b$
• C. $c$
• D. $\frac{1}{c}$

Answer 1

Answer: (A), (C)

$c$

$x^2+bx+c=0$
Sum of coefficients $=1+b+c=0$
Since, the sum of coefficients is zero, so the given quadratic equation has one root to be $1.$

Let another root be $\alpha .$
So, product of roots $=\frac{c}{1}$
$\Rightarrow 1\times \alpha =c$
$\Rightarrow \alpha =c$