Question
Find the polynomial having roots at $ 7 $ , $ 7 $ , $ -2 $ , $ -2 $ and $ -2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-8x^4-23x^3+134x^2+476x+392 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 7 $ | $ x-7 $ |
| $ 7 $ | $ x-7 $ |
| $ -2 $ | $ x+2 $ |
| $ -2 $ | $ x+2 $ |
| $ -2 $ | $ x+2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-7 \right) \cdot \left( x-7 \right) \cdot \left( x+2 \right) \cdot \left( x+2 \right) \cdot \left( x+2 \right) = x^5-8x^4-23x^3+134x^2+476x+392 $$This page was created using
Polynomial From Roots Calculator