Question
Find the polynomial having roots at $ \dfrac{ 51 }{ 10 } $ , $ \dfrac{ 27 }{ 10 } $ , $ \dfrac{ 3 }{ 2 } $ , $ \dfrac{ 9 }{ 10 } $ , $ \dfrac{ 3 }{ 5 } $ and $ \dfrac{ 9 }{ 20 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 200000x^6-2250000x^5+8964000x^4-16372800x^3+14696640x^2-6257007x+1003833 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 51 }{ 10 } $ | $ 10x-51 $ |
| $ \dfrac{ 27 }{ 10 } $ | $ 10x-27 $ |
| $ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
| $ \dfrac{ 9 }{ 10 } $ | $ 10x-9 $ |
| $ \dfrac{ 3 }{ 5 } $ | $ 5x-3 $ |
| $ \dfrac{ 9 }{ 20 } $ | $ 20x-9 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 10x-51 \right) \cdot \left( 10x-27 \right) \cdot \left( 2x-3 \right) \cdot \left( 10x-9 \right) \cdot \left( 5x-3 \right) \cdot \left( 20x-9 \right) = 200000x^6-2250000x^5+8964000x^4-16372800x^3+14696640x^2-6257007x+1003833 $$This page was created using
Polynomial From Roots Calculator