Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 7 } $ , $ -\dfrac{ 1 }{ 2 } $ , $ \dfrac{ 2 }{ 3 } $ and $ \dfrac{ 1 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 210x^4-107x^3-52x^2+23x-2 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 7 } $ | $ 7x-1 $ |
| $ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
| $ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
| $ \dfrac{ 1 }{ 5 } $ | $ 5x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 7x-1 \right) \cdot \left( 2x+1 \right) \cdot \left( 3x-2 \right) \cdot \left( 5x-1 \right) = 210x^4-107x^3-52x^2+23x-2 $$This page was created using
Polynomial From Roots Calculator