Question
Find the polynomial having roots at $ 7 $ , $ 4 $ , $ \dfrac{ 1 }{ 7 } $ and $ \dfrac{ 7 }{ 6 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 42x^4-517x^3+1788x^2-1617x+196 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 7 $ | $ x-7 $ |
| $ 4 $ | $ x-4 $ |
| $ \dfrac{ 1 }{ 7 } $ | $ 7x-1 $ |
| $ \dfrac{ 7 }{ 6 } $ | $ 6x-7 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-7 \right) \cdot \left( x-4 \right) \cdot \left( 7x-1 \right) \cdot \left( 6x-7 \right) = 42x^4-517x^3+1788x^2-1617x+196 $$This page was created using
Polynomial From Roots Calculator