Question
Find the polynomial having roots at $ 4 $ , $ 30 $ , $ \dfrac{ 1 }{ 8 } $ and $ 3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 8x^4-297x^3+1813x^2-3102x+360 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 4 $ | $ x-4 $ |
| $ 30 $ | $ x-30 $ |
| $ \dfrac{ 1 }{ 8 } $ | $ 8x-1 $ |
| $ 3 $ | $ x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-4 \right) \cdot \left( x-30 \right) \cdot \left( 8x-1 \right) \cdot \left( x-3 \right) = 8x^4-297x^3+1813x^2-3102x+360 $$This page was created using
Polynomial From Roots Calculator