Question
Find the polynomial having roots at $ \dfrac{ 15 }{ 2 } $ , $ \dfrac{ 16 }{ 5 } $ and $ -\dfrac{ 5 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 20x^3-164x^2-55x+1200 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 15 }{ 2 } $ | $ 2x-15 $ |
| $ \dfrac{ 16 }{ 5 } $ | $ 5x-16 $ |
| $ -\dfrac{ 5 }{ 2 } $ | $ 2x+5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-15 \right) \cdot \left( 5x-16 \right) \cdot \left( 2x+5 \right) = 20x^3-164x^2-55x+1200 $$This page was created using
Polynomial From Roots Calculator