Question
Find the polynomial having roots at $ 0 $ , $ 0 $ , $ 0 $ , $ 1 $ , $ 1 $ , $ \dfrac{ 3 }{ 2 } $ , $ 4 $ and $ 4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^8-23x^7+96x^6-179x^5+152x^4-48x^3 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 0 $ | $ x $ |
| $ 0 $ | $ x $ |
| $ 1 $ | $ x-1 $ |
| $ 1 $ | $ x-1 $ |
| $ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
| $ 4 $ | $ x-4 $ |
| $ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot x \cdot x \cdot \left( x-1 \right) \cdot \left( x-1 \right) \cdot \left( 2x-3 \right) \cdot \left( x-4 \right) \cdot \left( x-4 \right) = 2x^8-23x^7+96x^6-179x^5+152x^4-48x^3 $$This page was created using
Polynomial From Roots Calculator