Find the polynomial having roots at $ 1 $ , $ \dfrac{ 1 }{ 4 } $ , $ \dfrac{ 1 }{ 9 } $ and $ \dfrac{ 1 }{ 16 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 576x^4-820x^3+273x^2-30x+1 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ \dfrac{ 1 }{ 4 } $ | $ 4x-1 $ |
| $ \dfrac{ 1 }{ 9 } $ | $ 9x-1 $ |
| $ \dfrac{ 1 }{ 16 } $ | $ 16x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( 4x-1 \right) \cdot \left( 9x-1 \right) \cdot \left( 16x-1 \right) = 576x^4-820x^3+273x^2-30x+1 $$This page was created using
Polynomial From Roots Calculator