Question
Find the polynomial having roots at $ 3 $ , $ 5 $ , $ 9 $ , $ 17 $ , $ 33 $ and $ 53 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6-120x^5+5049x^4-93416x^3+798723x^2-3020256x+4013955 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ 5 $ | $ x-5 $ |
| $ 9 $ | $ x-9 $ |
| $ 17 $ | $ x-17 $ |
| $ 33 $ | $ x-33 $ |
| $ 53 $ | $ x-53 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( x-5 \right) \cdot \left( x-9 \right) \cdot \left( x-17 \right) \cdot \left( x-33 \right) \cdot \left( x-53 \right) = x^6-120x^5+5049x^4-93416x^3+798723x^2-3020256x+4013955 $$This page was created using
Polynomial From Roots Calculator