Question
Find the polynomial having roots at $ -5 $ , $ \dfrac{ 2 }{ 3 } $ and $ -\dfrac{ 5 }{ 7 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 21x^3+106x^2-5x-50 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -5 $ | $ x+5 $ |
| $ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
| $ -\dfrac{ 5 }{ 7 } $ | $ 7x+5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+5 \right) \cdot \left( 3x-2 \right) \cdot \left( 7x+5 \right) = 21x^3+106x^2-5x-50 $$This page was created using
Polynomial From Roots Calculator