How do you find the polynomial function with roots 1, –2, and 5?

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How do you find the polynomial function with roots 1, –2, and 5?

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Answer 1 · 2015-05-21T02:33:40

There is more than one polynomial function with roots $1$ $1$ , $- 2$ $-2$ and $5$ $5$ , but if those are the only roots, and none of them is root more than once, the function is:
$p (x) = (x - 1) \cdot (x - (- 2)) \cdot (x - 5) =$ $p(x) = (x-1) * (x-(-2)) * (x-5) =$
$= x^{3} - 4 \cdot x^{2} - 7 \cdot x + 10$ $=x^3 - 4*x^2 - 7*x + 10$

If you ever want to find a polynomial that has $x_{1}$ $x_1$ , $x_{2}$ $x_2$ ,..., $x_{n}$ $x_n$ as roots:
$p(x) = (x-x_1) * (x-x_2) * ... * (x-x_n)$

Hope it helps

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How do you find the polynomial function with roots 1, –2, and 5?

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