Find the polynomial having roots at $ 2 $ , $ -\dfrac{ 1 }{ 2 } $ and $ \dfrac{ 5 }{ 3 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 6x^3-19x^2+9x+10 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
| $ \dfrac{ 5 }{ 3 } $ | $ 3x-5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( 2x+1 \right) \cdot \left( 3x-5 \right) = 6x^3-19x^2+9x+10 $$This page was created using
Polynomial From Roots Calculator