Question
Find the polynomial having roots at $ -1 $ , $ -2 $ , $ \dfrac{ 2 }{ 5 } $ , $ -\dfrac{ 1 }{ 3 } $ and $ 3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 15x^5-x^4-107x^3-83x^2+20x+12 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ -2 $ | $ x+2 $ |
| $ \dfrac{ 2 }{ 5 } $ | $ 5x-2 $ |
| $ -\dfrac{ 1 }{ 3 } $ | $ 3x+1 $ |
| $ 3 $ | $ x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x+2 \right) \cdot \left( 5x-2 \right) \cdot \left( 3x+1 \right) \cdot \left( x-3 \right) = 15x^5-x^4-107x^3-83x^2+20x+12 $$This page was created using
Polynomial From Roots Calculator