Find the polynomial having roots at $ \dfrac{ 3 }{ 4 } $ , $ -3 $ and $ 2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 4x^3+x^2-27x+18 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 3 }{ 4 } $ | $ 4x-3 $ |
| $ -3 $ | $ x+3 $ |
| $ 2 $ | $ x-2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 4x-3 \right) \cdot \left( x+3 \right) \cdot \left( x-2 \right) = 4x^3+x^2-27x+18 $$This page was created using
Polynomial From Roots Calculator