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2. What are all the possible rational roots of the polynomial P(x) = 5* + 2003 + 2x2 +4?
0, +1, +2, +4
+1, +2, +4, +8
+1, +2, +4
+1, +2

Sagot :

Step-by-step explanation:

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (the coefficient of the constant term) is 7" role="presentation" style="margin: 0px; padding: 0px; box-sizing: border-box; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; font-size: 16px; line-height: normal; font-family: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">77.

Find its factors (with the plus sign and the minus sign): ±1" role="presentation" style="margin: 0px; padding: 0px; box-sizing: border-box; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; font-size: 16px; line-height: normal; font-family: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">±1±1, ±7" role="presentation" style="margin: 0px; padding: 0px; box-sizing: border-box; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; font-size: 16px; line-height: normal; font-family: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">±7±7.

These are the possible values for p" role="presentation" style="margin: 0px; padding: 0px; box-sizing: border-box; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; font-size: 16px; line-height: normal; font-family: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">pp.

The leading coefficient (the coefficient of the term with the highest degree) is 2" role="presentation" style="margin: 0px; padding: 0px; box-sizing: border-box; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; font-size: 16px; line-height: normal; font-family: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal;

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