Question
Find the polynomial having roots at $ 3 $ , $ \dfrac{ 3 }{ 4 } $ and $ 1 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 4x^3-19x^2+24x-9 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ \dfrac{ 3 }{ 4 } $ | $ 4x-3 $ |
| $ 1 $ | $ x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( 4x-3 \right) \cdot \left( x-1 \right) = 4x^3-19x^2+24x-9 $$This page was created using
Polynomial From Roots Calculator