Question
Find the polynomial having roots at $ 6 $ , $ -\dfrac{ 5 }{ 2 } $ and $ \dfrac{ 4 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 10x^3-43x^2-122x+120 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 6 $ | $ x-6 $ |
| $ -\dfrac{ 5 }{ 2 } $ | $ 2x+5 $ |
| $ \dfrac{ 4 }{ 5 } $ | $ 5x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-6 \right) \cdot \left( 2x+5 \right) \cdot \left( 5x-4 \right) = 10x^3-43x^2-122x+120 $$This page was created using
Polynomial From Roots Calculator