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Question
If x = – 4 is a root of Δ = `|(x, 2, 3),(1, x, 1),(3, 2, x)|` = 0, then find the other two roots.
Solution
Applying R1 → (R1 + R2 + R3), we get
`|(x + 4, x + 4, x + 4),(1, x, 1),(3, 2, x)|`
Taking (x + 4) common from R1, we get
Δ = `(x + 4) |(1, 1, 1),(1, x, 1),(3, 2, x)|`
Applying C2 → C2 – C1, C3 → C3 – C1 , we get
Δ = `(x + 4)|(1, 0, 0),(1, x - 1, 0),(3, -1, x - 3)|`
Expanding along R1,
∆ = (x + 4)[(x – 1)(x – 3) – 0].
Thus, ∆ = 0 implies x = – 4, 1, 3.
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