Find the polynomial having roots at $ \dfrac{ 4 }{ 5 } $ , $ -2 $ and $ \dfrac{ 7 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 10x^3-23x^2-58x+56 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 4 }{ 5 } $ | $ 5x-4 $ |
| $ -2 $ | $ x+2 $ |
| $ \dfrac{ 7 }{ 2 } $ | $ 2x-7 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5x-4 \right) \cdot \left( x+2 \right) \cdot \left( 2x-7 \right) = 10x^3-23x^2-58x+56 $$This page was created using
Polynomial From Roots Calculator