Question
Find the polynomial having roots at $ -2 $ , $ 4 $ , $ \dfrac{ 1 }{ 2 } $ , $ \dfrac{ 5 }{ 3 } $ and $ -\dfrac{ 1 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 12x^5-44x^4-59x^3+171x^2+14x-40 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -2 $ | $ x+2 $ |
| $ 4 $ | $ x-4 $ |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ \dfrac{ 5 }{ 3 } $ | $ 3x-5 $ |
| $ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+2 \right) \cdot \left( x-4 \right) \cdot \left( 2x-1 \right) \cdot \left( 3x-5 \right) \cdot \left( 2x+1 \right) = 12x^5-44x^4-59x^3+171x^2+14x-40 $$This page was created using
Polynomial From Roots Calculator