Question
Find the polynomial having roots at $ 15 $ , $ 30 $ , $ 45 $ , $ 75 $ and $ 100 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-265x^4+25725x^3-1128375x^2+22106250x-151875000 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 15 $ | $ x-15 $ |
| $ 30 $ | $ x-30 $ |
| $ 45 $ | $ x-45 $ |
| $ 75 $ | $ x-75 $ |
| $ 100 $ | $ x-100 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-15 \right) \cdot \left( x-30 \right) \cdot \left( x-45 \right) \cdot \left( x-75 \right) \cdot \left( x-100 \right) = x^5-265x^4+25725x^3-1128375x^2+22106250x-151875000 $$This page was created using
Polynomial From Roots Calculator