Find the polynomial having roots at $ 2 $ , $ -4 $ , $ \dfrac{ 3 }{ 2 } $ and $ -\dfrac{ 1 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 4x^4+4x^3-43x^2+26x+24 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ -4 $ | $ x+4 $ |
| $ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
| $ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x+4 \right) \cdot \left( 2x-3 \right) \cdot \left( 2x+1 \right) = 4x^4+4x^3-43x^2+26x+24 $$This page was created using
Polynomial From Roots Calculator