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Question Number 32357 by .none. last updated on 23/Mar/18

x^2 +ax−24=0 root is integer a range i cant speak english well. sorry

x2+ax−24=0rootisintegerarangeicantspeakenglishwell.sorry

Answered by mrW2 last updated on 23/Mar/18

let p, q be the integer roots. pq=−24 a=−(p+q) if pq=−24=−1×24: p=−1, q=24⇒a=−(−1+24)=−23 or p=1, q=−24⇒a=−(1−24)=23 or p=24, q=−1⇒a=−(24−1)=−23 or p=−24, q=1⇒a=−(−24+1)=23 ⇒a=±23 similarly, 24=2×12⇒a=±10 24=3×8⇒a=±5 24=4×6⇒a=±2

letp,qbetheintegerroots.pq=−24a=−(p+q)ifpq=−24=−1×24:p=−1,q=24⇒a=−(−1+24)=−23orp=1,q=−24⇒a=−(1−24)=23orp=24,q=−1⇒a=−(24−1)=−23orp=−24,q=1⇒a=−(−24+1)=23⇒a=±23similarly,24=2×12⇒a=±1024=3×8⇒a=±524=4×6⇒a=±2

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