Find the polynomial having roots at $ 2 $ , $ 0 $ , $ -3 $ , $ 0 $ , $ -6 $ , $ 0 $ , $ -2 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^8+9x^7+14x^6-36x^5-72x^4 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ 0 $ | $ x $ |
| $ -3 $ | $ x+3 $ |
| $ 0 $ | $ x $ |
| $ -6 $ | $ x+6 $ |
| $ 0 $ | $ x $ |
| $ -2 $ | $ x+2 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot x \cdot \left( x+3 \right) \cdot x \cdot \left( x+6 \right) \cdot x \cdot \left( x+2 \right) \cdot x = x^8+9x^7+14x^6-36x^5-72x^4 $$This page was created using
Polynomial From Roots Calculator