Question
Find the polynomial having roots at $ 1 $ , $ 4 $ , $ 9 $ , $ 16 $ and $ 25 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-55x^4+1023x^3-7645x^2+21076x-14400 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 4 $ | $ x-4 $ |
| $ 9 $ | $ x-9 $ |
| $ 16 $ | $ x-16 $ |
| $ 25 $ | $ x-25 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-4 \right) \cdot \left( x-9 \right) \cdot \left( x-16 \right) \cdot \left( x-25 \right) = x^5-55x^4+1023x^3-7645x^2+21076x-14400 $$This page was created using
Polynomial From Roots Calculator