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If (x – 1) and (x + 3) are the factors of x2 + k1x + k2 then
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- k1 = –2, k2 = –3
- k1 = 2, k2 = –3
- k1 = 2, k2 = 3
- k1 = –2, k2 = 3
Correct Option: B
f (x) = x² +k1x + k1
(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 equation (i),
k1 + k2 = –1
⇒ 2 + k2 = –1
⇒ k2 = –1 – 2 = –3
