Question
Find the polynomial having roots at $ 0 $ , $ \dfrac{ 1 }{ 100 } $ , $ \dfrac{ 1 }{ 10 } $ , $ 1 $ and $ 10 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 1000x^5-11110x^4+11211x^3-1111x^2+10x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ \dfrac{ 1 }{ 100 } $ | $ 100x-1 $ |
| $ \dfrac{ 1 }{ 10 } $ | $ 10x-1 $ |
| $ 1 $ | $ x-1 $ |
| $ 10 $ | $ x-10 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( 100x-1 \right) \cdot \left( 10x-1 \right) \cdot \left( x-1 \right) \cdot \left( x-10 \right) = 1000x^5-11110x^4+11211x^3-1111x^2+10x $$This page was created using
Polynomial From Roots Calculator