Find the polynomial having roots at $ -\dfrac{ 1 }{ 3 } $ , $ -1 $ , $ -1 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 3x^4+7x^3+5x^2+x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 1 }{ 3 } $ | $ 3x+1 $ |
| $ -1 $ | $ x+1 $ |
| $ -1 $ | $ x+1 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x+1 \right) \cdot \left( x+1 \right) \cdot \left( x+1 \right) \cdot x = 3x^4+7x^3+5x^2+x $$This page was created using
Polynomial From Roots Calculator