x^4-7x^3+25x^2-9x+87=0

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to find the roots of polynomial equation, hence you may use rational roots test.

You need to form the set of possible rational roots of polynomial equation such that: `{+-1;+-3;+-29;+-87}`

You need to substitute -1 for x in equation such that:

`1+7+25+9+87!=0`

You need to substitute 1 for x in equation such that:

`1-7+25-9+87!=0` You need to substitute 3 for x in equation such that: `81-189+225-27+87!=0` You need to substitute 29 for x in equation such that: `707281 - 170723 + 6525 - 261 + 87!=0` Notice that none of the values in set `{+-1;+-3;+-29;+-87` } does represent the roots of equation. You need to keep on searching the roots of polynomial, hence you need to sketch the graph of the polynomial function to check if it intercepts x axis such that: Notice that the graph intercepts y axis only, hence the polynomial is never zero: `x^4-7x^3+25x^2-9x+87!=0` .

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