Find the value of m for which the equation (m + 4)x 2 + (m + 1)x + 1 = 0 has real and equal roots.

Since, equation has equal roots, D = 0. ∴ b 2 - 4ac = 0 ⇒ (m + 1) 2 - 4(m + 4)(1) = 0 ⇒ m 2 + 1 + 2m - 4m - 16 = 0 ⇒ m 2 - 2m - 15 = 0 ⇒ m 2 - 5m + 3m - 15 = 0 ⇒ m(m - 5) + 3(m - 5) = 0 ⇒ (m + 3)(m - 5) = 0 ⇒ (m + 3) = 0 or (m - 5) = 0 ⇒ m = -3 or m = 5. Hence, m = -3 or 5.

Mathematics

Find the value of m for which the equation (m + 4)x² + (m + 1)x + 1 = 0 has real and equal roots.

Quadratic Equations

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Answer

Since, equation has equal roots, D = 0.

∴ b² - 4ac = 0

⇒ (m + 1)² - 4(m + 4)(1) = 0

⇒ m² + 1 + 2m - 4m - 16 = 0

⇒ m² - 2m - 15 = 0

⇒ m² - 5m + 3m - 15 = 0

⇒ m(m - 5) + 3(m - 5) = 0

⇒ (m + 3)(m - 5) = 0

⇒ (m + 3) = 0 or (m - 5) = 0

⇒ m = -3 or m = 5.

Hence, m = -3 or 5.

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Find the value of m for which the equation (m + 4)x² + (m + 1)x + 1 = 0 has real and equal roots.

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Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.

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Answer

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