Question
Find the polynomial having roots at $ 0 $ , $ 3 $ , $ \dfrac{ 9 }{ 2 } $ and $ 10 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^4-35x^3+177x^2-270x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ 3 $ | $ x-3 $ |
| $ \dfrac{ 9 }{ 2 } $ | $ 2x-9 $ |
| $ 10 $ | $ x-10 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( x-3 \right) \cdot \left( 2x-9 \right) \cdot \left( x-10 \right) = 2x^4-35x^3+177x^2-270x $$This page was created using
Polynomial From Roots Calculator