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+570x^2+932x-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:
$$ P(x) = \left( 3x-2 \right) \cdot \left( x-6 \right) \cdot \left( x-7 \right) \cdot \left( x+2 \right) \cdot \left( x+5 \right) = 3x^5-20x^4-105x^3+570x^2+932x-840 $$This page was created using
Polynomial From Roots Calculator