Find the polynomial having roots at $ \dfrac{ 1 }{ 2 } $ , $ \dfrac{ 3 }{ 2 } $ , $ 3 $ , $ \dfrac{ 13 }{ 2 } $ and $ 5 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 8x^5-132x^4+774x^3-1939x^2+1962x-585 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
| $ 3 $ | $ x-3 $ |
| $ \dfrac{ 13 }{ 2 } $ | $ 2x-13 $ |
| $ 5 $ | $ x-5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-1 \right) \cdot \left( 2x-3 \right) \cdot \left( x-3 \right) \cdot \left( 2x-13 \right) \cdot \left( x-5 \right) = 8x^5-132x^4+774x^3-1939x^2+1962x-585 $$This page was created using
Polynomial From Roots Calculator