Question
Find the polynomial having roots at $ 0 $ , $ 90 $ , $ 180 $ , $ 270 $ and $ 360 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-900x^4+283500x^3-36450000x^2+1574640000x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 90 $ | $ x-90 $ |
| $ 180 $ | $ x-180 $ |
| $ 270 $ | $ x-270 $ |
| $ 360 $ | $ x-360 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( x-90 \right) \cdot \left( x-180 \right) \cdot \left( x-270 \right) \cdot \left( x-360 \right) = x^5-900x^4+283500x^3-36450000x^2+1574640000x $$This page was created using
Polynomial From Roots Calculator