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x-4-4x-3-8x-1-m-0-has-4-real-roots-find-m-

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Question Number 199654 by hardmath last updated on 06/Nov/23
x^4 + 4x^3 − 8x + 1 − m = 0 has 4 real roots find m=?
x4+4x3−8x+1−m=0has4realrootsfindm=?
Answered by Frix last updated on 07/Nov/23
This can be factorized and thus solved x=−1±(√(3±(√(m+3)))) [4 combinations of signs] ⇒ m+3>0∧3−(√(m+3))>0 ⇒ −3<m<6
Thiscanbefactorizedandthussolvedx=−1±3±m+3[4combinationsofsigns]⇒m+3>0∧3−m+3>0⇒−3<m<6

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