Question
Find the polynomial having roots at $ 0 $ , $ 4 $ , $ 3 $ , $ 1 $ , $ 0 $ , $ 14 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^7-22x^6+131x^5-278x^4+168x^3 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 4 $ | $ x-4 $ |
| $ 3 $ | $ x-3 $ |
| $ 1 $ | $ x-1 $ |
| $ 0 $ | $ x $ |
| $ 14 $ | $ x-14 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( x-4 \right) \cdot \left( x-3 \right) \cdot \left( x-1 \right) \cdot x \cdot \left( x-14 \right) \cdot x = x^7-22x^6+131x^5-278x^4+168x^3 $$This page was created using
Polynomial From Roots Calculator