Question
Find the polynomial having roots at $ 1 $ , $ 2 $ , $ 4 $ , $ 8 $ , $ 16 $ , $ 32 $ and $ 64 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^7-127x^6+5334x^5-94488x^4+755904x^3-2731008x^2+4161536x-2097152 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 2 $ | $ x-2 $ |
| $ 4 $ | $ x-4 $ |
| $ 8 $ | $ x-8 $ |
| $ 16 $ | $ x-16 $ |
| $ 32 $ | $ x-32 $ |
| $ 64 $ | $ x-64 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( x-4 \right) \cdot \left( x-8 \right) \cdot \left( x-16 \right) \cdot \left( x-32 \right) \cdot \left( x-64 \right) = x^7-127x^6+5334x^5-94488x^4+755904x^3-2731008x^2+4161536x-2097152 $$This page was created using
Polynomial From Roots Calculator