Find the polynomial having roots at $ 3 $ , $ 6 $ , $ -4 $ and $ 2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^4-7x^3-8x^2+108x-144 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ 6 $ | $ x-6 $ |
| $ -4 $ | $ x+4 $ |
| $ 2 $ | $ x-2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( x-6 \right) \cdot \left( x+4 \right) \cdot \left( x-2 \right) = x^4-7x^3-8x^2+108x-144 $$This page was created using
Polynomial From Roots Calculator