Question
Find the polynomial having roots at $ -1 $ , $ 5 $ , $ \dfrac{ 56 }{ 25 } $ and $ -\dfrac{ 56 }{ 25 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 625x^4-2500x^3-6261x^2+12544x+15680 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 5 $ | $ x-5 $ |
| $ \dfrac{ 56 }{ 25 } $ | $ 25x-56 $ |
| $ -\dfrac{ 56 }{ 25 } $ | $ 25x+56 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x-5 \right) \cdot \left( 25x-56 \right) \cdot \left( 25x+56 \right) = 625x^4-2500x^3-6261x^2+12544x+15680 $$This page was created using
Polynomial From Roots Calculator