Question
Find the polynomial having roots at $ 3 $ , $ -7 $ , $ 2 $ and $ -\dfrac{ 1 }{ 3 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 3x^4+7x^3-85x^2+97x+42 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 3 $ | $ x-3 $ |
| $ -7 $ | $ x+7 $ |
| $ 2 $ | $ x-2 $ |
| $ -\dfrac{ 1 }{ 3 } $ | $ 3x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-3 \right) \cdot \left( x+7 \right) \cdot \left( x-2 \right) \cdot \left( 3x+1 \right) = 3x^4+7x^3-85x^2+97x+42 $$This page was created using
Polynomial From Roots Calculator