Question

If the quadratic equation $a{x}^2+bx+c=0$ has $-2$ as one of its roots then $x+by+c=0$ represents

• A. A family of concurrent lines
• B. A family of parallel lines
• C. A single line
• D. A line perpendicular to x-axis

Answer 1

The correct option is A A family of concurrent lines

Given

$a{x}^2+bx+c=0$

One root is $-2$

$-2+\alpha =\frac{-b}{a}-----\left(1\right)$

$-2\alpha =\frac{c}{a}---\left(2\right)$

On solving eq (1) and (2)

$c=2(a+b)$

Given eq

$x+by+c=0$

$x+by+2a+2b=0$

Hence above equation represents family of lines