Question
Find the polynomial having roots at $ 2 $ , $ \dfrac{ 1 }{ 2 } $ , $ -5 $ , $ 8 $ , $ -4 $ and $ -\dfrac{ 1 }{ 3 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 6x^6-7x^5-324x^4-281x^3+2030x^2-264x-320 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ -5 $ | $ x+5 $ |
| $ 8 $ | $ x-8 $ |
| $ -4 $ | $ x+4 $ |
| $ -\dfrac{ 1 }{ 3 } $ | $ 3x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( 2x-1 \right) \cdot \left( x+5 \right) \cdot \left( x-8 \right) \cdot \left( x+4 \right) \cdot \left( 3x+1 \right) = 6x^6-7x^5-324x^4-281x^3+2030x^2-264x-320 $$This page was created using
Polynomial From Roots Calculator