Question
Find the polynomial having roots at $ 1 $ , $ 8 $ , $ -\dfrac{ 1 }{ 8 } $ and $ -\dfrac{ 1 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 40x^4-347x^3+204x^2+95x+8 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 8 $ | $ x-8 $ |
| $ -\dfrac{ 1 }{ 8 } $ | $ 8x+1 $ |
| $ -\dfrac{ 1 }{ 5 } $ | $ 5x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-8 \right) \cdot \left( 8x+1 \right) \cdot \left( 5x+1 \right) = 40x^4-347x^3+204x^2+95x+8 $$This page was created using
Polynomial From Roots Calculator