Question
Find the polynomial having roots at $ -\dfrac{ 5 }{ 2 } $ , $ 1 $ , $ 5 $ and $ 5 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^4-17x^3+15x^2+125x-125 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 5 }{ 2 } $ | $ 2x+5 $ |
| $ 1 $ | $ x-1 $ |
| $ 5 $ | $ x-5 $ |
| $ 5 $ | $ x-5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x+5 \right) \cdot \left( x-1 \right) \cdot \left( x-5 \right) \cdot \left( x-5 \right) = 2x^4-17x^3+15x^2+125x-125 $$This page was created using
Polynomial From Roots Calculator