Find the polynomial having roots at $ -\dfrac{ 1 }{ 3 } $ , $ 2 $ , $ 4 $ and $ 6 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 3x^4-35x^3+120x^2-100x-48 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 1 }{ 3 } $ | $ 3x+1 $ |
| $ 2 $ | $ x-2 $ |
| $ 4 $ | $ x-4 $ |
| $ 6 $ | $ x-6 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x+1 \right) \cdot \left( x-2 \right) \cdot \left( x-4 \right) \cdot \left( x-6 \right) = 3x^4-35x^3+120x^2-100x-48 $$This page was created using
Polynomial From Roots Calculator