Find the polynomial having roots at $ 1 $ , $ 12 $ , $ 3 $ and $ -3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-13x^3+3x^2+117x-108 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 12 $ | $ x-12 $ |
| $ 3 $ | $ x-3 $ |
| $ -3 $ | $ x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-12 \right) \cdot \left( x-3 \right) \cdot \left( x+3 \right) = x^4-13x^3+3x^2+117x-108 $$This page was created using
Polynomial From Roots Calculator