Find the polynomial having roots at $ 14 $ , $ 21 $ , $ -6 $ , $ 12 $ and $ \dfrac{ 1 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^5-83x^4+905x^3+1080x^2-43092x+21168 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 14 $ | $ x-14 $ |
| $ 21 $ | $ x-21 $ |
| $ -6 $ | $ x+6 $ |
| $ 12 $ | $ x-12 $ |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-14 \right) \cdot \left( x-21 \right) \cdot \left( x+6 \right) \cdot \left( x-12 \right) \cdot \left( 2x-1 \right) = 2x^5-83x^4+905x^3+1080x^2-43092x+21168 $$This page was created using
Polynomial From Roots Calculator