Question
Find the polynomial having roots at $ 3 $ , $ 7 $ , $ -\dfrac{ 5 }{ 7 } $ and $ 2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 7x^4-79x^3+227x^2-89x-210 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ 7 $ | $ x-7 $ |
| $ -\dfrac{ 5 }{ 7 } $ | $ 7x+5 $ |
| $ 2 $ | $ x-2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( x-7 \right) \cdot \left( 7x+5 \right) \cdot \left( x-2 \right) = 7x^4-79x^3+227x^2-89x-210 $$This page was created using
Polynomial From Roots Calculator