Question
Find the polynomial having roots at $ -10 $ , $ -2 $ , $ 40 $ and $ \dfrac{ 1001 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 5x^4-1141x^3+25728x^2+456460x+800800 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -10 $ | $ x+10 $ |
| $ -2 $ | $ x+2 $ |
| $ 40 $ | $ x-40 $ |
| $ \dfrac{ 1001 }{ 5 } $ | $ 5x-1001 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+10 \right) \cdot \left( x+2 \right) \cdot \left( x-40 \right) \cdot \left( 5x-1001 \right) = 5x^4-1141x^3+25728x^2+456460x+800800 $$This page was created using
Polynomial From Roots Calculator