Find the polynomial having roots at $ -3 $ , $ -1 $ , $ 2 $ and $ \dfrac{ 1 }{ 7 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 7x^4+13x^3-37x^2-37x+6 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -3 $ | $ x+3 $ |
| $ -1 $ | $ x+1 $ |
| $ 2 $ | $ x-2 $ |
| $ \dfrac{ 1 }{ 7 } $ | $ 7x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+3 \right) \cdot \left( x+1 \right) \cdot \left( x-2 \right) \cdot \left( 7x-1 \right) = 7x^4+13x^3-37x^2-37x+6 $$This page was created using
Polynomial From Roots Calculator