Question
Find the polynomial having roots at $ 1 $ , $ -1 $ , $ 13 $ , $ \dfrac{ 1 }{ 13 } $ , $ 17 $ and $ \dfrac{ 1 }{ 17 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 221x^6-6660x^5+49521x^4-49521x^2+6660x-221 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ -1 $ | $ x+1 $ |
| $ 13 $ | $ x-13 $ |
| $ \dfrac{ 1 }{ 13 } $ | $ 13x-1 $ |
| $ 17 $ | $ x-17 $ |
| $ \dfrac{ 1 }{ 17 } $ | $ 17x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x+1 \right) \cdot \left( x-13 \right) \cdot \left( 13x-1 \right) \cdot \left( x-17 \right) \cdot \left( 17x-1 \right) = 221x^6-6660x^5+49521x^4-49521x^2+6660x-221 $$This page was created using
Polynomial From Roots Calculator