Question
Find the polynomial having roots at $ -\dfrac{ 2 }{ 3 } $ , $ -1 $ , $ 2 $ , $ -2 $ and $ -3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 3x^5+14x^4+5x^3-50x^2-68x-24 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 2 }{ 3 } $ | $ 3x+2 $ |
| $ -1 $ | $ x+1 $ |
| $ 2 $ | $ x-2 $ |
| $ -2 $ | $ x+2 $ |
| $ -3 $ | $ x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x+2 \right) \cdot \left( x+1 \right) \cdot \left( x-2 \right) \cdot \left( x+2 \right) \cdot \left( x+3 \right) = 3x^5+14x^4+5x^3-50x^2-68x-24 $$This page was created using
Polynomial From Roots Calculator