Question
Find the polynomial having roots at $ \dfrac{ 5 }{ 3 } $ , $ -\dfrac{ 5 }{ 2 } $ and $ \dfrac{ 1 }{ 4 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 24x^3+14x^2-105x+25 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 5 }{ 3 } $ | $ 3x-5 $ |
| $ -\dfrac{ 5 }{ 2 } $ | $ 2x+5 $ |
| $ \dfrac{ 1 }{ 4 } $ | $ 4x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x-5 \right) \cdot \left( 2x+5 \right) \cdot \left( 4x-1 \right) = 24x^3+14x^2-105x+25 $$This page was created using
Polynomial From Roots Calculator