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Multiple Choice Questions

If x ndash 1 and x 3 are the factor of x2 k1x k2 then ........

Mathematics (NDA) Algebra

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If (x – 1) and (x + 3) are the factor of x² + k₁x + k₂ then

k₁ = –2, k₂ = –3

k₁ = 2, k₂ = –3

k₁ = 2, k₂ = 3

k₁ = –2, k₂ = 3

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Explanation:

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.