Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 2 } $ , $ \dfrac{ 2 }{ 3 } $ , $ 1 $ , $ 2 $ and $ -2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 6x^5-13x^4-15x^3+50x^2-36x+8 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
| $ 1 $ | $ x-1 $ |
| $ 2 $ | $ x-2 $ |
| $ -2 $ | $ x+2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-1 \right) \cdot \left( 3x-2 \right) \cdot \left( x-1 \right) \cdot \left( x-2 \right) \cdot \left( x+2 \right) = 6x^5-13x^4-15x^3+50x^2-36x+8 $$This page was created using
Polynomial From Roots Calculator