Question
Find the polynomial having roots at $ 1 $ , $ -3 $ , $ \dfrac{ 1 }{ 2 } $ and $ -\dfrac{ 3 }{ 4 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 8x^4+18x^3-23x^2-12x+9 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ -3 $ | $ x+3 $ |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ -\dfrac{ 3 }{ 4 } $ | $ 4x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x+3 \right) \cdot \left( 2x-1 \right) \cdot \left( 4x+3 \right) = 8x^4+18x^3-23x^2-12x+9 $$This page was created using
Polynomial From Roots Calculator