Question
Find the polynomial having roots at $ \dfrac{ 17 }{ 2 } $ , $ 8 $ , $ \dfrac{ 35 }{ 4 } $ and $ 9 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 8x^4-274x^3+3517x^2-20051x+42840 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 17 }{ 2 } $ | $ 2x-17 $ |
| $ 8 $ | $ x-8 $ |
| $ \dfrac{ 35 }{ 4 } $ | $ 4x-35 $ |
| $ 9 $ | $ x-9 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-17 \right) \cdot \left( x-8 \right) \cdot \left( 4x-35 \right) \cdot \left( x-9 \right) = 8x^4-274x^3+3517x^2-20051x+42840 $$This page was created using
Polynomial From Roots Calculator