Question
Find the polynomial having roots at $ -1 $ , $ -3 $ , $ -\dfrac{ 1 }{ 100 } $ and $ -\dfrac{ 1 }{ 200 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 20000x^4+80300x^3+61201x^2+904x+3 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ -3 $ | $ x+3 $ |
| $ -\dfrac{ 1 }{ 100 } $ | $ 100x+1 $ |
| $ -\dfrac{ 1 }{ 200 } $ | $ 200x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x+3 \right) \cdot \left( 100x+1 \right) \cdot \left( 200x+1 \right) = 20000x^4+80300x^3+61201x^2+904x+3 $$This page was created using
Polynomial From Roots Calculator