Question

The value of m for which the equation x² + 2(m + 1)x + m² = 0 has equal roots is *
The value of m for which the equation x² + 2(m + 1)x + m² = 0 has equal roots is *





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Answer 1

Equation given: x^2 + 2mx + m - 2x + 5 = 0

(rewriting the equation)

x^2 + (2mx – 2x) + (m + 5) = 0

x^2 + 2(m - 1)x + (m + 5) = 0 ---------- ①

For the roots to be equal, the discriminant (D = b^2 – 4ac) must equal 0,

i.e.,

b^2 – 4ac = 0 ,

Where, a = 1, b = 2(m – 1), c = (m + 5)

[2(m – 1)]^2 – 4(1)(m + 5) = 0,

4(m^2 – 2m + 1) – 4(m + 5) = 0,

(m^2 – 2m + 1) – (m + 5) = 0,

m^2 – 2m + 1 – m – 5 = 0,

m^2 – 3m – 4 = 0,

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