Question
Find the polynomial having roots at $ 0 $ , $ 1 $ , $ \dfrac{ 5 }{ 2 } $ , $ \dfrac{ 7 }{ 2 } $ and $ 5 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 4x^5-48x^4+199x^3-330x^2+175x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 1 $ | $ x-1 $ |
| $ \dfrac{ 5 }{ 2 } $ | $ 2x-5 $ |
| $ \dfrac{ 7 }{ 2 } $ | $ 2x-7 $ |
| $ 5 $ | $ x-5 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( x-1 \right) \cdot \left( 2x-5 \right) \cdot \left( 2x-7 \right) \cdot \left( x-5 \right) = 4x^5-48x^4+199x^3-330x^2+175x $$This page was created using
Polynomial From Roots Calculator