Question
Find the polynomial having roots at $ -\dfrac{ 2 }{ 3 } $ , $ -6 $ , $ 7 $ , $ -2 $ and $ -5 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 3x^5+20x^4-105x^3-990x^2-1868x-840 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 2 }{ 3 } $ | $ 3x+2 $ |
| $ -6 $ | $ x+6 $ |
| $ 7 $ | $ x-7 $ |
| $ -2 $ | $ x+2 $ |
| $ -5 $ | $ x+5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x+2 \right) \cdot \left( x+6 \right) \cdot \left( x-7 \right) \cdot \left( x+2 \right) \cdot \left( x+5 \right) = 3x^5+20x^4-105x^3-990x^2-1868x-840 $$This page was created using
Polynomial From Roots Calculator