Question
Find the polynomial having roots at $ 1 $ , $ 8 $ , $ 18 $ and $ 15 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-42x^3+575x^2-2694x+2160 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 8 $ | $ x-8 $ |
| $ 18 $ | $ x-18 $ |
| $ 15 $ | $ x-15 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-8 \right) \cdot \left( x-18 \right) \cdot \left( x-15 \right) = x^4-42x^3+575x^2-2694x+2160 $$This page was created using
Polynomial From Roots Calculator