Find the polynomial having roots at $ 5 $ , $ 0 $ , $ 5 $ and $ 7 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-17x^3+95x^2-175x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 5 $ | $ x-5 $ |
| $ 0 $ | $ x $ |
| $ 5 $ | $ x-5 $ |
| $ 7 $ | $ x-7 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-5 \right) \cdot x \cdot \left( x-5 \right) \cdot \left( x-7 \right) = x^4-17x^3+95x^2-175x $$This page was created using
Polynomial From Roots Calculator