Question
Find the polynomial having roots at $ 0 $ , $ \dfrac{ 9 }{ 5 } $ , $ -\dfrac{ 2 }{ 5 } $ and $ -\dfrac{ 8 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 125x^4+25x^3-370x^2-144x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ \dfrac{ 9 }{ 5 } $ | $ 5x-9 $ |
| $ -\dfrac{ 2 }{ 5 } $ | $ 5x+2 $ |
| $ -\dfrac{ 8 }{ 5 } $ | $ 5x+8 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( 5x-9 \right) \cdot \left( 5x+2 \right) \cdot \left( 5x+8 \right) = 125x^4+25x^3-370x^2-144x $$This page was created using
Polynomial From Roots Calculator