Question
Find the polynomial having roots at $ 0 $ , $ \dfrac{ 1 }{ 4 } $ , $ \dfrac{ 1 }{ 2 } $ and $ 1 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 8x^4-14x^3+7x^2-x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ \dfrac{ 1 }{ 4 } $ | $ 4x-1 $ |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ 1 $ | $ x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( 4x-1 \right) \cdot \left( 2x-1 \right) \cdot \left( x-1 \right) = 8x^4-14x^3+7x^2-x $$This page was created using
Polynomial From Roots Calculator