Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 3 } $ , $ 100 $ , $ 15 $ , $ 67 $ and $ 69 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 3x^5-754x^4+65540x^3-2228698x^2+21539145x-6934500 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 3 } $ | $ 3x-1 $ |
| $ 100 $ | $ x-100 $ |
| $ 15 $ | $ x-15 $ |
| $ 67 $ | $ x-67 $ |
| $ 69 $ | $ x-69 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x-1 \right) \cdot \left( x-100 \right) \cdot \left( x-15 \right) \cdot \left( x-67 \right) \cdot \left( x-69 \right) = 3x^5-754x^4+65540x^3-2228698x^2+21539145x-6934500 $$This page was created using
Polynomial From Roots Calculator