Question
Find the polynomial having roots at $ -\dfrac{ 11 }{ 4 } $ , $ 4 $ , $ 1 $ and $ 1 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 4x^4-13x^3-30x^2+83x-44 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 11 }{ 4 } $ | $ 4x+11 $ |
| $ 4 $ | $ x-4 $ |
| $ 1 $ | $ x-1 $ |
| $ 1 $ | $ x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 4x+11 \right) \cdot \left( x-4 \right) \cdot \left( x-1 \right) \cdot \left( x-1 \right) = 4x^4-13x^3-30x^2+83x-44 $$This page was created using
Polynomial From Roots Calculator