Question
Find the polynomial having roots at $ \dfrac{ 13 }{ 500 } $ , $ \dfrac{ 1 }{ 20 } $ , $ -\dfrac{ 13 }{ 500 } $ and $ -\dfrac{ 1 }{ 20 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 100000000x^4-317600x^2+169 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 13 }{ 500 } $ | $ 500x-13 $ |
| $ \dfrac{ 1 }{ 20 } $ | $ 20x-1 $ |
| $ -\dfrac{ 13 }{ 500 } $ | $ 500x+13 $ |
| $ -\dfrac{ 1 }{ 20 } $ | $ 20x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 500x-13 \right) \cdot \left( 20x-1 \right) \cdot \left( 500x+13 \right) \cdot \left( 20x+1 \right) = 100000000x^4-317600x^2+169 $$This page was created using
Polynomial From Roots Calculator