Question
Find the polynomial having roots at $ -5 $ , $ -3 $ , $ \dfrac{ 1 }{ 2 } $ and $ 4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^4+7x^3-38x^2-103x+60 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -5 $ | $ x+5 $ |
| $ -3 $ | $ x+3 $ |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+5 \right) \cdot \left( x+3 \right) \cdot \left( 2x-1 \right) \cdot \left( x-4 \right) = 2x^4+7x^3-38x^2-103x+60 $$This page was created using
Polynomial From Roots Calculator