Question

If the equation $a{x}^2+bx+c=0$ is not altered when each of the coefficient is increased by same quantity, then the value of $x^2+x+1$ is

Answer 1

$a{x}^2+bx+c=0$
Let the coefficient be increased by $k,(k\ne 0)$, then
$(a+k)x^2+(b+k)x+(c+k)=0$
$\Rightarrow a{x}^2+bx+c+k{x}^2+kx+k=0$
$\Rightarrow 0+k(x^2+x+1)=0$
$\Rightarrow x^2+x+1=0(\because k\ne 0)$