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