Question
Find the polynomial having roots at $ 1 $ , $ -\dfrac{ 5 }{ 2 } $ and $ -3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^3+9x^2+4x-15 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ -\dfrac{ 5 }{ 2 } $ | $ 2x+5 $ |
| $ -3 $ | $ x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( 2x+5 \right) \cdot \left( x+3 \right) = 2x^3+9x^2+4x-15 $$This page was created using
Polynomial From Roots Calculator