Question
Find the polynomial having roots at $ 9 $ , $ 7 $ , $ 0 $ , $ -3 $ and $ 8 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-21x^4+119x^3+69x^2-1512x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 9 $ | $ x-9 $ |
| $ 7 $ | $ x-7 $ |
| $ 0 $ | $ x $ |
| $ -3 $ | $ x+3 $ |
| $ 8 $ | $ x-8 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-9 \right) \cdot \left( x-7 \right) \cdot x \cdot \left( x+3 \right) \cdot \left( x-8 \right) = x^5-21x^4+119x^3+69x^2-1512x $$This page was created using
Polynomial From Roots Calculator