Find the polynomial having roots at $ 2 $ , $ \dfrac{ 47 }{ 10 } $ , $ -6 $ and $ 18 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 10x^4-187x^3-182x^2+6108x-10152 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ \dfrac{ 47 }{ 10 } $ | $ 10x-47 $ |
| $ -6 $ | $ x+6 $ |
| $ 18 $ | $ x-18 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( 10x-47 \right) \cdot \left( x+6 \right) \cdot \left( x-18 \right) = 10x^4-187x^3-182x^2+6108x-10152 $$This page was created using
Polynomial From Roots Calculator