Question
Find the polynomial having roots at $ 2 $ , $ -2 $ , $ 3 $ and $ \dfrac{ 3 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 5x^4-18x^3-11x^2+72x-36 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ -2 $ | $ x+2 $ |
| $ 3 $ | $ x-3 $ |
| $ \dfrac{ 3 }{ 5 } $ | $ 5x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x+2 \right) \cdot \left( x-3 \right) \cdot \left( 5x-3 \right) = 5x^4-18x^3-11x^2+72x-36 $$This page was created using
Polynomial From Roots Calculator