Question
Find the polynomial having roots at $ 2 $ , $ 8 $ , $ -9 $ , $ 10 $ and $ 22 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-33x^4+178x^3+2292x^2-20888x+31680 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ 8 $ | $ x-8 $ |
| $ -9 $ | $ x+9 $ |
| $ 10 $ | $ x-10 $ |
| $ 22 $ | $ x-22 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x-8 \right) \cdot \left( x+9 \right) \cdot \left( x-10 \right) \cdot \left( x-22 \right) = x^5-33x^4+178x^3+2292x^2-20888x+31680 $$This page was created using
Polynomial From Roots Calculator