Question
Find the polynomial having roots at $ 3 $ , $ 0 $ , $ 2 $ , $ 21 $ , $ 3 $ , $ 1 $ , $ 0 $ , $ \dfrac{ 3 }{ 2 } $ , $ 2 $ , $ 3 $ , $ 3 $ and $ 2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^{12}-83x^{11}+1230x^{10}-9661x^9+46432x^8-145425x^7+303606x^6-419499x^5+368226x^4-185652x^3+40824x^2 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ 0 $ | $ x $ |
| $ 2 $ | $ x-2 $ |
| $ 21 $ | $ x-21 $ |
| $ 3 $ | $ x-3 $ |
| $ 1 $ | $ x-1 $ |
| $ 0 $ | $ x $ |
| $ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
| $ 2 $ | $ x-2 $ |
| $ 3 $ | $ x-3 $ |
| $ 3 $ | $ x-3 $ |
| $ 2 $ | $ x-2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot x \cdot \left( x-2 \right) \cdot \left( x-21 \right) \cdot \left( x-3 \right) \cdot \left( x-1 \right) \cdot x \cdot \left( 2x-3 \right) \cdot \left( x-2 \right) \cdot \left( x-3 \right) \cdot \left( x-3 \right) \cdot \left( x-2 \right) = 2x^{12}-83x^{11}+1230x^{10}-9661x^9+46432x^8-145425x^7+303606x^6-419499x^5+368226x^4-185652x^3+40824x^2 $$This page was created using
Polynomial From Roots Calculator