Question
Find the polynomial having roots at $ -\dfrac{ 1 }{ 2 } $ , $ -3 $ , $ 3 $ and $ \dfrac{ 1 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 4x^4-37x^2+9 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
| $ -3 $ | $ x+3 $ |
| $ 3 $ | $ x-3 $ |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x+1 \right) \cdot \left( x+3 \right) \cdot \left( x-3 \right) \cdot \left( 2x-1 \right) = 4x^4-37x^2+9 $$This page was created using
Polynomial From Roots Calculator