Find the polynomial having roots at $ -2 $ , $ -\dfrac{ 5 }{ 2 } $ and $ -1 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^3+11x^2+19x+10 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -2 $ | $ x+2 $ |
| $ -\dfrac{ 5 }{ 2 } $ | $ 2x+5 $ |
| $ -1 $ | $ x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+2 \right) \cdot \left( 2x+5 \right) \cdot \left( x+1 \right) = 2x^3+11x^2+19x+10 $$This page was created using
Polynomial From Roots Calculator