Find the polynomial having roots at $ -\dfrac{ 1 }{ 2 } $ , $ \dfrac{ 1 }{ 3 } $ and $ \dfrac{ 4 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 30x^3-19x^2-9x+4 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
| $ \dfrac{ 1 }{ 3 } $ | $ 3x-1 $ |
| $ \dfrac{ 4 }{ 5 } $ | $ 5x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x+1 \right) \cdot \left( 3x-1 \right) \cdot \left( 5x-4 \right) = 30x^3-19x^2-9x+4 $$This page was created using
Polynomial From Roots Calculator