Question

If (x – 2) is a common factor of the expressions x² + ax + b and x² + cx + d, then \(\frac{b-d}{c-a}\) is equal to 

(a) –2 

(b) –1 

(c) 1 

(d) 2

Answer 1

(d) 2

(x – 2) is a common factor of (x² + ax + b) and (x² + cx + d) 

⇒ 4 + 2a + b = 0                 ...(i) 

and 4 + 2c + d = 0             ...(ii)

∴ 2a + b = 2c + d ⇒ b – d = 2(c – a) ⇒ \(\frac{b-d}{c-a}\) = 2.