Without solving the following quadratic equation, find the value of ‘m’ for which the given equation has real and equal roots.

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asked Feb 9 in Class X Maths by muskan15 (-1,583 points)

Without solving the following quadratic equation, find the value of ‘m’ for which the given equation has real and equal roots.

x2 + 2(m – 1)x + (m + 5) = 0

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answered Feb 9 by navnit40 (-1,146 points)

x2 + 2(m – 1)x + (m + 5) = 0

Equating with ax2 + bx + c = 0

a = 1, b = 2(m – 1), c = (m + 5)

Since equation has real and equal roots.

So,  D = 0

⇒ b2 – 4ac = 0

[2(m – 1)2 – 4 × 1 × (m + 5) = 0

⇒ 4(m – 1)2 – 4(m + 5) = 0

⇒ 4 [(m – 1)2 – (m + 5)] = 0

⇒ 4 [m2 – 2m + 1 – m – 5] = 0

⇒ m2 – 3m – 4 = 0

⇒ (m + 1)(m – 4) = 0

Either     m + 1 = 0

m = - 1

or       m – 4 = 0

m = 4

m = -1, 4

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