Question
Find the polynomial having roots at $ -\dfrac{ 2 }{ 5 } $ , $ 1 $ , $ 2 $ , $ -1 $ , $ 5 $ and $ -\dfrac{ 2 }{ 3 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 15x^6-89x^5+27x^4+221x^3-2x^2-132x-40 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 2 }{ 5 } $ | $ 5x+2 $ |
| $ 1 $ | $ x-1 $ |
| $ 2 $ | $ x-2 $ |
| $ -1 $ | $ x+1 $ |
| $ 5 $ | $ x-5 $ |
| $ -\dfrac{ 2 }{ 3 } $ | $ 3x+2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5x+2 \right) \cdot \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( x+1 \right) \cdot \left( x-5 \right) \cdot \left( 3x+2 \right) = 15x^6-89x^5+27x^4+221x^3-2x^2-132x-40 $$This page was created using
Polynomial From Roots Calculator