Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 2 } $ , $ -2 $ , $ 3 $ and $ -4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^4+5x^3-23x^2-38x+24 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ -2 $ | $ x+2 $ |
| $ 3 $ | $ x-3 $ |
| $ -4 $ | $ x+4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-1 \right) \cdot \left( x+2 \right) \cdot \left( x-3 \right) \cdot \left( x+4 \right) = 2x^4+5x^3-23x^2-38x+24 $$This page was created using
Polynomial From Roots Calculator