Question
Find the polynomial having roots at $ 3 $ , $ -5 $ , $ 2 $ , $ -8 $ and $ 7 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5+x^4-75x^3+11x^2+1094x-1680 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ -5 $ | $ x+5 $ |
| $ 2 $ | $ x-2 $ |
| $ -8 $ | $ x+8 $ |
| $ 7 $ | $ x-7 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( x+5 \right) \cdot \left( x-2 \right) \cdot \left( x+8 \right) \cdot \left( x-7 \right) = x^5+x^4-75x^3+11x^2+1094x-1680 $$This page was created using
Polynomial From Roots Calculator