Question
Find the polynomial having roots at $ -1 $ , $ 3 $ , $ 7 $ and $ -\dfrac{ 1 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^4-17x^3+13x^2+53x+21 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 3 $ | $ x-3 $ |
| $ 7 $ | $ x-7 $ |
| $ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x-3 \right) \cdot \left( x-7 \right) \cdot \left( 2x+1 \right) = 2x^4-17x^3+13x^2+53x+21 $$This page was created using
Polynomial From Roots Calculator