Question
Find the polynomial having roots at $ -2 $ , $ -\dfrac{ 2 }{ 5 } $ and $ 5 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 5x^3-13x^2-56x-20 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -2 $ | $ x+2 $ |
| $ -\dfrac{ 2 }{ 5 } $ | $ 5x+2 $ |
| $ 5 $ | $ x-5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+2 \right) \cdot \left( 5x+2 \right) \cdot \left( x-5 \right) = 5x^3-13x^2-56x-20 $$This page was created using
Polynomial From Roots Calculator