Find the polynomial having roots at $ 7 $ , $ 4 $ , $ -4 $ , $ -7 $ and $ -9 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5+9x^4-65x^3-585x^2+784x+7056 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 7 $ | $ x-7 $ |
| $ 4 $ | $ x-4 $ |
| $ -4 $ | $ x+4 $ |
| $ -7 $ | $ x+7 $ |
| $ -9 $ | $ x+9 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-7 \right) \cdot \left( x-4 \right) \cdot \left( x+4 \right) \cdot \left( x+7 \right) \cdot \left( x+9 \right) = x^5+9x^4-65x^3-585x^2+784x+7056 $$This page was created using
Polynomial From Roots Calculator