Find the polynomial having roots at $ 6 $ , $ \dfrac{ 23 }{ 10 } $ , $ 17 $ and $ 12 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 10x^4-373x^3+4585x^2-20934x+28152 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 6 $ | $ x-6 $ |
| $ \dfrac{ 23 }{ 10 } $ | $ 10x-23 $ |
| $ 17 $ | $ x-17 $ |
| $ 12 $ | $ x-12 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-6 \right) \cdot \left( 10x-23 \right) \cdot \left( x-17 \right) \cdot \left( x-12 \right) = 10x^4-373x^3+4585x^2-20934x+28152 $$This page was created using
Polynomial From Roots Calculator