Find the polynomial having roots at $ 5 $ , $ 2 $ , $ 10 $ and $ 4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-21x^3+148x^2-420x+400 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 5 $ | $ x-5 $ |
| $ 2 $ | $ x-2 $ |
| $ 10 $ | $ x-10 $ |
| $ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-5 \right) \cdot \left( x-2 \right) \cdot \left( x-10 \right) \cdot \left( x-4 \right) = x^4-21x^3+148x^2-420x+400 $$This page was created using
Polynomial From Roots Calculator