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If the characteristic equation of the differential equation d²y/dx² + 2α dy/dx + y = 0 has two equal roots, then the values of α are

1. ±1
2. 0,0
3. ±j
4. ±1/2

Correct answer: ±1

Solution

Characteristic equation is r^2 + 2(alpha)r + 1 = 0. Equal roots require discriminant (2 alpha)^2 - 4 = 0, so alpha^2 = 1 and alpha = +/-1. Correct option is +/-1, not +/-1/2.

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