Find the polynomial having roots at $ \dfrac{ 29 }{ 10 } $ , $ -2 $ , $ -\dfrac{ 1 }{ 2 } $ and $ 2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 20x^4-48x^3-109x^2+192x+116 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 29 }{ 10 } $ | $ 10x-29 $ |
| $ -2 $ | $ x+2 $ |
| $ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
| $ 2 $ | $ x-2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 10x-29 \right) \cdot \left( x+2 \right) \cdot \left( 2x+1 \right) \cdot \left( x-2 \right) = 20x^4-48x^3-109x^2+192x+116 $$This page was created using
Polynomial From Roots Calculator