Question
Find the polynomial having roots at $ -5 $ , $ -2 $ , $ 3 $ and $ 90 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-86x^3-371x^2+960x+2700 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -5 $ | $ x+5 $ |
| $ -2 $ | $ x+2 $ |
| $ 3 $ | $ x-3 $ |
| $ 90 $ | $ x-90 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+5 \right) \cdot \left( x+2 \right) \cdot \left( x-3 \right) \cdot \left( x-90 \right) = x^4-86x^3-371x^2+960x+2700 $$This page was created using
Polynomial From Roots Calculator