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Let P(x0=x^3-8x^2+c x-d be a polynomial ...

Let `P(x0=x^3-8x^2+c x-d` be a polynomial with real coefficients and with all it roots being distinct positive integers. Then number of possible value of `c` is___________.

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The correct Answer is:
36
We have `x_(1)+x_(2)+x_(3)=8`
`x_(1)+x_(2)+x_(3)=d`
`x_(1)x_(2)+x_(2)x_(3)+x_(3)x_(1)=c`
Possible roots `1,2,5or1,3,4`
`:.d=10ord=12`
`impliesc=2+10+5=17or3+12+4=19`
Hence, `d=10andc=17ord=12andc=19`
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