Question
Find the polynomial having roots at $ 0 $ , $ \dfrac{ 9 }{ 2 } $ , $ 4 $ and $ 7 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^4-31x^3+155x^2-252x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ \dfrac{ 9 }{ 2 } $ | $ 2x-9 $ |
| $ 4 $ | $ x-4 $ |
| $ 7 $ | $ x-7 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( 2x-9 \right) \cdot \left( x-4 \right) \cdot \left( x-7 \right) = 2x^4-31x^3+155x^2-252x $$This page was created using
Polynomial From Roots Calculator