f(x) = x2 + k1x + k2 (x – 1) is a factor of f(x) . ∴ f(1) = 0 ⇒ 1 + k1 + k2 = 0 ⇒ k1 + k2 = –1 ...(i) Again, f(–3) = 0 ⇒ (–3)2 + k1(–3) + k2 = 0 ⇒ 9 – 3k1 + k2 = 0 ⇒ 3k1 – k2 = 9 ...(ii) On adding both equations, 4k1 = 8
⇒ k1 = 2 From eq.(i) , k1 + k2 = –1 ⇒ 2 + k2 = –1
⇒ k2 = –3. |