Question
Find the polynomial having roots at $ \dfrac{ 3 }{ 5 } $ , $ -10 $ , $ 1 $ and $ -3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 5x^4+57x^3+49x^2-201x+90 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 3 }{ 5 } $ | $ 5x-3 $ |
| $ -10 $ | $ x+10 $ |
| $ 1 $ | $ x-1 $ |
| $ -3 $ | $ x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5x-3 \right) \cdot \left( x+10 \right) \cdot \left( x-1 \right) \cdot \left( x+3 \right) = 5x^4+57x^3+49x^2-201x+90 $$This page was created using
Polynomial From Roots Calculator