Find the polynomial having roots at $ 2 $ , $ \dfrac{ 1 }{ 2 } $ and $ 6 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^3-17x^2+32x-12 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ 6 $ | $ x-6 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( 2x-1 \right) \cdot \left( x-6 \right) = 2x^3-17x^2+32x-12 $$This page was created using
Polynomial From Roots Calculator