Question
Find the polynomial having roots at $ 2 $ , $ -\dfrac{ 4 }{ 3 } $ and $ \dfrac{ 4 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 15x^3-22x^2-32x+32 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ -\dfrac{ 4 }{ 3 } $ | $ 3x+4 $ |
| $ \dfrac{ 4 }{ 5 } $ | $ 5x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( 3x+4 \right) \cdot \left( 5x-4 \right) = 15x^3-22x^2-32x+32 $$This page was created using
Polynomial From Roots Calculator