Find the polynomial having roots at $ \dfrac{ 1 }{ 3 } $ , $ 2 $ , $ 4 $ and $ 10 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 3x^4-49x^3+220x^2-308x+80 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 3 } $ | $ 3x-1 $ |
| $ 2 $ | $ x-2 $ |
| $ 4 $ | $ x-4 $ |
| $ 10 $ | $ x-10 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x-1 \right) \cdot \left( x-2 \right) \cdot \left( x-4 \right) \cdot \left( x-10 \right) = 3x^4-49x^3+220x^2-308x+80 $$This page was created using
Polynomial From Roots Calculator