Find the polynomial having roots at $ -1 $ , $ 1 $ , $ \dfrac{ 3 }{ 2 } $ , $ \dfrac{ 3 }{ 2 } $ , $ -2 $ and $ -\dfrac{ 1 }{ 3 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 12x^6-8x^5-61x^4+47x^3+67x^2-39x-18 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 1 $ | $ x-1 $ |
| $ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
| $ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
| $ -2 $ | $ x+2 $ |
| $ -\dfrac{ 1 }{ 3 } $ | $ 3x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x-1 \right) \cdot \left( 2x-3 \right) \cdot \left( 2x-3 \right) \cdot \left( x+2 \right) \cdot \left( 3x+1 \right) = 12x^6-8x^5-61x^4+47x^3+67x^2-39x-18 $$This page was created using
Polynomial From Roots Calculator