Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 2 } $ , $ 9 $ , $ -\dfrac{ 1 }{ 2 } $ and $ 6 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 4x^4-60x^3+215x^2+15x-54 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ 9 $ | $ x-9 $ |
| $ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
| $ 6 $ | $ x-6 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-1 \right) \cdot \left( x-9 \right) \cdot \left( 2x+1 \right) \cdot \left( x-6 \right) = 4x^4-60x^3+215x^2+15x-54 $$This page was created using
Polynomial From Roots Calculator