Question
Find the polynomial having roots at $ -\dfrac{ 7 }{ 3 } $ , $ -2 $ , $ 0 $ , $ \dfrac{ 1 }{ 2 } $ , $ \dfrac{ 1 }{ 2 } $ and $ \dfrac{ 3 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 24x^6+44x^5-106x^4-107x^3+157x^2-42x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 7 }{ 3 } $ | $ 3x+7 $ |
| $ -2 $ | $ x+2 $ |
| $ 0 $ | $ x $ |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x+7 \right) \cdot \left( x+2 \right) \cdot x \cdot \left( 2x-1 \right) \cdot \left( 2x-1 \right) \cdot \left( 2x-3 \right) = 24x^6+44x^5-106x^4-107x^3+157x^2-42x $$This page was created using
Polynomial From Roots Calculator