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Let P(x)=x3−8x2+cx−d be a polynomial with real coefficients and with all its roots being distinct positive integers. Then the sum of all possible values of c is _________.

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Detailed Solution

We have x1+x2+x3=8x1x2x3=dx1x2+x2x3+x3x1=cPossible roots 1, 2, 5 or 1, 3, 4∴ d=10 or d=12⇒ c=2+10+5=17 or 3+12+4=19Hence, d = 10 and c = 17 or d = 12 and c = 19

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Let P(x)=x3−8x2+cx−d be a polynomial with real coefficients and with all its roots being distinct positive integers. Then the sum of all possible values of c is _________.