Find the polynomial having roots at $ -1 $ , $ 7 $ , $ 3 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-9x^3+11x^2+21x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 7 $ | $ x-7 $ |
| $ 3 $ | $ x-3 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x-7 \right) \cdot \left( x-3 \right) \cdot x = x^4-9x^3+11x^2+21x $$This page was created using
Polynomial From Roots Calculator