Question
Find the polynomial having roots at $ 10 $ , $ 12 $ , $ 14 $ and $ \dfrac{ 9 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^4-81x^3+1180x^2-7212x+15120 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 10 $ | $ x-10 $ |
| $ 12 $ | $ x-12 $ |
| $ 14 $ | $ x-14 $ |
| $ \dfrac{ 9 }{ 2 } $ | $ 2x-9 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-10 \right) \cdot \left( x-12 \right) \cdot \left( x-14 \right) \cdot \left( 2x-9 \right) = 2x^4-81x^3+1180x^2-7212x+15120 $$This page was created using
Polynomial From Roots Calculator