Find the polynomial having roots at $ 7 $ , $ 7 $ , $ 5 $ and $ 9 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-28x^3+290x^2-1316x+2205 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 7 $ | $ x-7 $ |
| $ 7 $ | $ x-7 $ |
| $ 5 $ | $ x-5 $ |
| $ 9 $ | $ x-9 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-7 \right) \cdot \left( x-7 \right) \cdot \left( x-5 \right) \cdot \left( x-9 \right) = x^4-28x^3+290x^2-1316x+2205 $$This page was created using
Polynomial From Roots Calculator