Question
Find the polynomial having roots at $ 4 $ , $ -\dfrac{ 3 }{ 4 } $ and $ -2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 4x^3-5x^2-38x-24 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 4 $ | $ x-4 $ |
| $ -\dfrac{ 3 }{ 4 } $ | $ 4x+3 $ |
| $ -2 $ | $ x+2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-4 \right) \cdot \left( 4x+3 \right) \cdot \left( x+2 \right) = 4x^3-5x^2-38x-24 $$This page was created using
Polynomial From Roots Calculator