Question
Find the polynomial having roots at $ 3 $ , $ -2 $ , $ 6 $ , $ \dfrac{ 2 }{ 5 } $ , $ \dfrac{ 5 }{ 2 } $ , $ -5 $ and $ 3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 10x^7-79x^6-135x^5+2201x^4-3659x^3-6078x^2+16380x-5400 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ -2 $ | $ x+2 $ |
| $ 6 $ | $ x-6 $ |
| $ \dfrac{ 2 }{ 5 } $ | $ 5x-2 $ |
| $ \dfrac{ 5 }{ 2 } $ | $ 2x-5 $ |
| $ -5 $ | $ x+5 $ |
| $ 3 $ | $ x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( x+2 \right) \cdot \left( x-6 \right) \cdot \left( 5x-2 \right) \cdot \left( 2x-5 \right) \cdot \left( x+5 \right) \cdot \left( x-3 \right) = 10x^7-79x^6-135x^5+2201x^4-3659x^3-6078x^2+16380x-5400 $$This page was created using
Polynomial From Roots Calculator