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Solutions: m = −2, m = −8, m = −8
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If the solutions are m = −2, m = −8 (double), the cubic equation with those roots is
(m + 2)(m + 8)^2 = 0.
Expand:
(m + 8)^2 = m^2 + 16m + 64
(m + 2)(m^2 + 16m + 64) = m^3 + 18m^2 + 96m + 128 = 0.
Solve by factoring:
(m + 2)(m + 8)^2 = 0 ⇒ m = −2 or m = −8 (with multiplicity 2).
(m + 2)(m + 8)^2 = 0.
Expand:
(m + 8)^2 = m^2 + 16m + 64
(m + 2)(m^2 + 16m + 64) = m^3 + 18m^2 + 96m + 128 = 0.
Solve by factoring:
(m + 2)(m + 8)^2 = 0 ⇒ m = −2 or m = −8 (with multiplicity 2).
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