Find the polynomial having roots at $ \dfrac{ 3 }{ 5 } $ , $ -\dfrac{ 4 }{ 5 } $ and $ -5 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 25x^3+130x^2+13x-60 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 3 }{ 5 } $ | $ 5x-3 $ |
| $ -\dfrac{ 4 }{ 5 } $ | $ 5x+4 $ |
| $ -5 $ | $ x+5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5x-3 \right) \cdot \left( 5x+4 \right) \cdot \left( x+5 \right) = 25x^3+130x^2+13x-60 $$This page was created using
Polynomial From Roots Calculator