Find the polynomial having roots at $ -2 $ , $ 2 $ , $ -\dfrac{ 1 }{ 3 } $ , $ -4 $ , $ 1 $ and $ 1 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 3x^6+7x^5-31x^4-23x^3+80x^2-20x-16 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -2 $ | $ x+2 $ |
| $ 2 $ | $ x-2 $ |
| $ -\dfrac{ 1 }{ 3 } $ | $ 3x+1 $ |
| $ -4 $ | $ x+4 $ |
| $ 1 $ | $ x-1 $ |
| $ 1 $ | $ x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+2 \right) \cdot \left( x-2 \right) \cdot \left( 3x+1 \right) \cdot \left( x+4 \right) \cdot \left( x-1 \right) \cdot \left( x-1 \right) = 3x^6+7x^5-31x^4-23x^3+80x^2-20x-16 $$This page was created using
Polynomial From Roots Calculator