Question

If the quadratic equation \( a x^{2}+b x+c=0 \) has \( -2 \) as one of its roots then \( a x+b y+c=0 \) 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 

ax² + bx + c = 0

One root is −2

−2 + α = −b/a ​−−−(1)

−2α = c/a ​−−−(2)

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.