Question
Find the polynomial having roots at $ \dfrac{ 3 }{ 2 } $ , $ 3 $ and $ -\dfrac{ 4 }{ 3 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 6x^3-19x^2-9x+36 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
| $ 3 $ | $ x-3 $ |
| $ -\dfrac{ 4 }{ 3 } $ | $ 3x+4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-3 \right) \cdot \left( x-3 \right) \cdot \left( 3x+4 \right) = 6x^3-19x^2-9x+36 $$This page was created using
Polynomial From Roots Calculator