Find the polynomial having roots at $ 4 $ , $ 7 $ , $ 12 $ , $ 3 $ and $ 9 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-35x^4+463x^3-2877x^2+8352x-9072 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 4 $ | $ x-4 $ |
| $ 7 $ | $ x-7 $ |
| $ 12 $ | $ x-12 $ |
| $ 3 $ | $ x-3 $ |
| $ 9 $ | $ x-9 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-4 \right) \cdot \left( x-7 \right) \cdot \left( x-12 \right) \cdot \left( x-3 \right) \cdot \left( x-9 \right) = x^5-35x^4+463x^3-2877x^2+8352x-9072 $$This page was created using
Polynomial From Roots Calculator