Multiple choice

If the equations x2 + 2x + 3λ = 0 and 2x2 + 3x + 5λ = 0 have a common non-zero root, the value of λ is

  1. -1

  2. 1

  3. 3

  4. -3
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AI explanation

Let a1 = 1, b1 = 2 and c1 = 3λ for the first equation, and a2 = 2, b2 = 3 and c2 = 5λ for the second equation. The condition for two quadratic equations to have a common root is (a1b2 - a2b1)(b1c2 - b2c1) = (c1a2 - c2a1)2. Substituting the values gives (3 - 4)(10λ - 9λ) = (6λ2 - 5λ2), which simplifies to (-1)(λ) = (λ)2. Solving λ2 + λ = 0 yields λ = -1, since the root must be non-zero.

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