Question
Find the polynomial having roots at $ -7 $ , $ -4 $ , $ 17 $ and $ 76 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-82x^3+297x^2+11608x+36176 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -7 $ | $ x+7 $ |
| $ -4 $ | $ x+4 $ |
| $ 17 $ | $ x-17 $ |
| $ 76 $ | $ x-76 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+7 \right) \cdot \left( x+4 \right) \cdot \left( x-17 \right) \cdot \left( x-76 \right) = x^4-82x^3+297x^2+11608x+36176 $$This page was created using
Polynomial From Roots Calculator