Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 7 } $ , $ 9 $ , $ 8 $ , $ 8 $ , $ -6 $ , $ 7 $ and $ 5 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 7x^7-218x^6+2278x^5-5144x^4-65741x^3+464434x^2-911712x+120960 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 7 } $ | $ 7x-1 $ |
| $ 9 $ | $ x-9 $ |
| $ 8 $ | $ x-8 $ |
| $ 8 $ | $ x-8 $ |
| $ -6 $ | $ x+6 $ |
| $ 7 $ | $ x-7 $ |
| $ 5 $ | $ x-5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 7x-1 \right) \cdot \left( x-9 \right) \cdot \left( x-8 \right) \cdot \left( x-8 \right) \cdot \left( x+6 \right) \cdot \left( x-7 \right) \cdot \left( x-5 \right) = 7x^7-218x^6+2278x^5-5144x^4-65741x^3+464434x^2-911712x+120960 $$This page was created using
Polynomial From Roots Calculator